In an audio message published by his press service on the messenging app Telegram, Prigozhin said: "Today the settlement of Krasna Hora was taken by the assault troops of the Wagner private military company".
Prigozhin also published a short video, apparently showing Wagner fighters at the entrance sign to Krasna Hora, which had a pre-war population of 600.
Reuters could not independently verify that the village had been taken.
The Wagner Group, a once secretive mercenary force that fought for Moscow's allies in Africa and the Middle East, has for months spearheaded the assault on Bakhmut, making small but steady gains in a battle that has raged since last summer.
(Reporting by Reuters; Editing by Susan Fenton)