"We are very happy to learn that our comrades-in-arms are alive and well," the navy said on Facebook.
The Ukrainian soldiers had surrendered after running out of ammunition, it said.
Russia destroyed the entire infrastructure of the island.
Although Russia's defence ministry had said they were captured, Ukrainian officials assumed the 13 soldiers were dead after it lost connection with the island.
However, the Russian military later shared pictures of the prisoners.
Ukrainians online circulated an unverified recording on Friday of a Russian warship ordering a Ukrainian outpost on the island to surrender.
The Ukrainians reply: "Russian warship, go f*** yourself."
Ukraine President Volodymyr Zelenskiy had said the 13 guards had been killed by a Russian strike and would receive posthumous honours.
with reporting from Reuters