In a Facebook post, the armed forces general staff said Russia suffered the losses on Tuesday when Ukrainian forces shelled the village of Denezhnykove, 70 km (45 miles) behind front lines in the eastern province of Luhansk.
It gave no further detail. The Russian defence ministry did not immediately reply to a request for comment, and Reuters was unable to independently verify the Ukrainian military's account.
The United States has provided Ukraine with advanced rocket systems capable of hitting targets up to 80 km away.
Last month Chechen leader Ramzan Kadyrov, a close ally of Russian President Vladimir Putin, said 23 of his soldiers had been killed and another 58 wounded in a Ukrainian artillery barrage.
(Reporting by David LjunggrenEditing by Mark Heinrich)
A Ukrainian serviceman rides atop an APC as his unit travels in the Kherson area, 15 November 2022 (issued by 16 November) amid the Russian invasion. The Ukrainian army is pushing Russian troops from occupied territory in the south of the country in a counter attack. Russian troops entered Ukraine on 24 February 2022 starting a conflict that has provoked destruction and a humanitarian crisis. EPA-EFE/GEORGE IVANCHENKO