Three Su-34 fighter bombers were shot down over Kherson region, the Ukrainian air force announced.
President Volodymr Zelensky thanked the servicemen who had downed the planes, saying the incident had occurred in war-torn Kherson Region.
Moscow has not commented on the claims, but influential Russian bloggers have reported losses.
In his nightly address on Friday, Mr Zelensky said the downing of the planes would make Russian pilots attacking targets in Ukraine aware that "none of them [would] go unpunished".
He also said he had spoken to Dutch Prime Minister Mark Rutte about the future delivery of F-16 jets, as well as a new EU support package.
Russia has not commented on the reported loss of its jets, but Fighterbomber, an influential Russian war blogger, reported the loss of an unspecified number of planes, saying they had probably been downed by US-made Patriot missiles.
Both surviving and dead crew members were recovered, the blogger added.
Another blogger, Voenniy Osvedomitel, said the planes had probably been used to drop glide bombs on a Ukrainian position on the Russian-controlled side of the Dnipro River.
Ukraine is facing an ammunition shortage as it continues to fight occupying Russian forces, following Moscow's full-scale invasion in February 2022.
Kyiv's counter-offensive ground to a halt at the start of the winter, and Republican representatives in the US - by far Ukraine's largest military backer - have been reluctant to further fund Ukraine's war effort.
In a year-end press conference this week, Mr Zelensky insisted that Ukraine was not losing the war with Russia.
By Oliver Slow