The locomotive of the train travelling from the city of Zhytomyr, located west of Kyiv, to Odessa on the Black Sea caught fire due to the attack, according to the authorities.
None of the 593 passengers aboard the train, including 15 children, were injured, military governor Oleh Kiper said on Telegram.
They have since been brought to Odessa by bus, he added.
Kiper accused Russia of targeting the train deliberately, saying there had been a second attack as passengers were being taken away.
Earlier this month, a train driver and his assistant were killed in a Russian attack on a passenger train in the Odessa region.
Meanwhile, in the eastern Ukrainian region of Kharkiv, seven people were injured in another Russian drone attack, according to the authorities.
Ukraine's air defence recorded a total of 127 drone attacks, saying most of them had been repelled.
Ukraine also launched fresh drone attacks against Russia, leaving one person dead and six injured in the border region of Belgorod, according to the authorities.
The Russian defence ministry said on Sunday morning that a total of 328 Ukrainian drones were shot down.
It was not possible to independently verify the figures.
The debris of a downed drone hit a warehouse of Russian online retailer Ozon in Orenburg, near the Kazakh border, authorities said.
A fire broke out at the site and 300 people had to be relocated but no one was injured, the ministry said.
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