Deputy Defence Minister Hanna Maliar said 53 badly wounded soldiers were taken to the town of Novoazovsk, held by Russian-backed rebels.
She said another 211 were evacuated using a humanitarian corridor to Olenivka - also a rebel-held town.
Russia earlier said a deal had been reached to evacuate the injured troops.
About a dozen buses carrying Ukrainian fighters who were holed up beneath the besieged plant were seen leaving the huge industrial site in the southern port city on Monday evening, Reuters news agency reported.
Russian state-run media outlets also posted footage of what they say were injured Ukrainian soldiers being evacuated from Azovstal.
Ms Maliar said the troops would be exchanged for captured Russian soldiers.