The majority of the Ukrainians were badly wounded, suffering from gunshot and shrapnel wounds, blast traumas, burns, fractured bones and amputated limbs, the agency known by the acronym GUR said in a statement on Telegram.
There was no comment from Russia about a prisoner swap.
But the head of the self-proclaimed Donetsk People's Republic in eastern Ukraine said it had secured the release of 144 soldiers, including its fighters and those of the Russian army.
Hundreds more Ukrainians are still thought to be held by Russia and its pro-Moscow separatist proxies in eastern Ukraine, but their precise whereabouts are not known.
The prisoner swap included the handover of 43 members of the Azov regiment, a National Guard unit that Russia says is a dangerous far-right battalion, a promising sign for Ukrainians hoping for the release of other fighters from the unit.