ZAPORIZHZHIA, Ukraine—Last month, an armed group turned up at Dmitry Skorniakov’s farm close to Mariupol and told workers that the land was being “nationalized” and now belonged to them.

Moscow’s invasion of Ukraine has captured some of the most productive agricultural land in what is one of the world’s great breadbaskets, disrupting supplies and pushing up food prices. Russian forces have also stolen grain and equipment, the Ukrainian government and farmers say. Now, entire farms are being taken, some farmers say.

That allegation of land theft is becoming increasingly common in parts of Ukraine occupied by Russian forces, heaping more misery upon the country’s beleaguered farming industry and threatening to crimp harvests when the world needs Ukrainian crops.

Farmers say groups showing up at the farm gate have identified themselves variously as Russians, fighters in Ukraine helping the Russians and representatives of Ukraine’s pro-Kremlin breakaway regions.

Russia didn’t immediately comment on the alleged land thefts, and hasn’t previously directly addressed accusations of stolen grain.

Mr. Skorniakov said that in May a group arrived at his farm in southeastern Ukraine claiming to represent the government of the self-proclaimed Donetsk People’s Republic, which broke away from Ukraine with Russian support in 2014.

“They said, ‘Now it belongs to us and you work for us, everything is our property,’” Mr. Skorniakov said his workers had told him. Mr. Skorniakov owns a company that runs several farms across Ukraine and is based outside of the occupied territories.

Soon after that, other groups arrived, including one that claimed to represent a former Russian government minister, according to Mr. Skorniakov, who was told by a worker who witnessed it. In one instance, an argument ensued and shots were let off in the air, he said.

The DPR didn’t immediately comment.

Valery Stoyanov, 50, said Chechen soldiers took over his farm near the southern city of Melitopol shortly after the invasion began on Feb. 24, telling his farmhands that it now belonged to the unit’s commander.

Valery Stoyanov said Chechen soldiers took over his farm near the southern Ukrainian city of Melitopol.

“This collective farm is now mine,” the Chechen commander told workers whom he had gathered to address, Mr. Stoyanov said his workers told him.

In the following days, the soldiers sold valuable equipment and shipped out 2,500 tons of grain that was stored at the farm.

Mr. Stoyanov said neighbors told him that the soldiers were allowing some farmers to stay on land nearby, but that they had to give a large proportion of their profits to the Russians.

“They’ve told my workers not to expect me back any time soon because I’m on a list of people to be shot,” said Mr. Stoyanov, who has previously fought Russian proxies in eastern Ukraine.

Russia’s national guard, which Chechen forces are part of, didn’t immediately respond to a request for comment.

Sergey Porada, 51, broke his combine before he left his farm to Russian soldiers in the village of Fedorivka in Zaporizhzhia region. Now the soldiers are trying to get in touch with him to repair the machinery in time for the harvest, he said.

“I broke it for a reason,” he said, laughing.

Farmers in Zaporizhzhia region who have been evicted from their land.

Shell casing left by tank fire in Viktor Gryshchuk’s fields.

Managers at one of Petro Melnyk’s farms, in the occupied part of eastern Ukraine’s Luhansk region, were recently summoned by the new Russia-backed local government and told that there would be new management at the business, he said. Mr. Melnyk’s managers described the meeting to him in text messages and he hadn’t heard from them since. Russia has cut off access to Ukrainian cellphone networks in occupied areas, making contact harder.

“For more than two months I have had no information about them or what is happening on the farm,” said Mr. Melnyk, the chief executive and co-owner of Agricom Group, which owns farms across Ukraine.

Mr. Melnyk’s only clues come from looking at satellite images of his farm, from which he has concluded that crops have been planted.

Landowners who live outside of the occupied territories, or who have ties to Kyiv, are the ones losing their property, several farmers said, while those without connections and who still reside in the area have kept theirs.

Farmers are also sometimes taking over neighboring land, or threatening to, when their owners have fled to western Ukraine, some farmers said, leading to a climate of fear and mistrust across the farming community in the occupied territories.

A farmer in southern Ukraine said he left his 2,000-hectare farm at the start of March when Russian shelling hit his house. He now worries that it will be taken from him.

“Our towns are full of collaborators,” he said.

Neighbors have told him that Russian forces had already raided his stores of wheat and sunflower seeds.

Viktor Gryshchuk’s fields were once used as a position by Ukrainian forces.

Overall, the Ukrainian government has accused Russia of stealing around 400,000 metric tons of grains and seeds. Ukraine has also accused Russia of deliberately trying to hurt its farming sector, which generated about 22% of the country’s gross domestic product last year, according to United Nations data.

Farmers in northern parts of the country have said retreating Russian troops left mines on their land, destroyed buildings and took equipment, such as tractors and trucks.

A study by the Kyiv School of Economics released Wednesday estimated that the invasion has cost Ukraine’s farming sector $4.3 billion in destroyed equipment, damaged land and unharvested crops.

Since the beginning of the war, Viktor Gryshchuk, 64, has tried to keep his 1,000-hectare farm running between Russian and Ukrainian lines in Zaporizhzhia region. Rocket and mortar fire has already chewed holes through his grain silos and pockmarked his fields.

“They throw incendiary ammunition so the fields burn, they aim at the crops intentionally, they also aim at our warehouses,” he said against the sound of shelling in the distance. “If they can drive us out eventually they figure the land will be theirs.”

Farmers hanging on to their land in the occupied territories have other problems, including contending with lowball pricing from what they describe as carpetbaggers from Crimea, which Moscow annexed in 2014.

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Andrii Gogolev, whose farm is in a part of southern Ukraine currently occupied, recently sold his stock of soy for $296 a metric ton, down from the more than $500 it was bringing in before the war. Mr. Gogolev said several agricultural dealers with Crimean accents had shown up to buy produce. His strawberries and cherries were also getting low offers.

A grain trader from Crimea said he had been contacting farmers in the region and offering between $100 and $130 for a ton of grain, which he said is about half the going market rate. Farmers also have to work out their own transport to Crimea to deliver the grain.

He said dozens of other traders like him were doing the same.

Given the inability to sell outside of Ukraine because of the occupation, some farmers say they have little choice but to sell at these prices.

“There is a hard depression around farmers,” said Mr. Gogolev.

Viktor Gryshchuk’s farm has been damaged by rocket and mortar fire since the beginning of the war.

—Hanna Oliinyk contributed to this article.

Write to Alistair MacDonald at alistair.macdonald@wsj.com and Thomas Grove at thomas.grove@wsj.com