There was no immediate comment from Russia's defence ministry and a local Ukrainian official denied Kadyrov's claim.
Sumy region lies on Ukraine's northern border and has not seen a major Russian ground assault since the beginning of the conflict in 2022.
Kadyrov said fighters from his Akhmat battalion "together with servicemen from other Russian units carried out tactical operations and liberated another settlement from the enemy."
"It is the village of Ryzhivka, which is on the border with the Kursk region," the Chechen leader said in a post on Telegram.
"As a result of large-scale planned offensive actions, the Ukrainian side suffered significant losses and was forced to retreat," he added.
AFP was not able to immediately verify Kadyrov's battlefield claims.
Yuriy Zarko, the Ukrainian head of the local municipality, later denied Ryzhivka had been captured and told state broadcaster Suspilne there were no Russian troops in the village.
Ukrainian President Volodymyr Zelensky warned last month Russia was amassing troops along the northern border ahead of what might be a new offensive.
Authorities began evacuating residents living in some border towns and villages in the Sumy region last month, citing the risk of increased Russian attacks.
On May 10, Russia began a major ground operation in the neighbouring Kharkiv region, capturing several towns and villages as Kyiv's forces struggle with manpower and ammunition shortages.
Ukraine has since rushed reinforcements to the area but lost ground to Russia elsewhere on the front, with Zelensky warning on Sunday of difficult battles in the eastern Donetsk region.
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