Another 15 people were wounded in the daytime attack, seven of them children, said Oleh Syniehubov, head of the Kharkiv regional administration.
Ukrainian Interior Minister Ivan Vyhovsky said the strike hit at a time when many people were in the park, including families with children. He said a cafe building was also damaged.
Initial reports put the death toll at three, among them an infant in a stroller. Nova Vodolaha lies southwest of Kharkiv, dozens of kilometres from the front line.
In the early hours of 19 October, the Russian army carried out a combined strike on Kyiv and the surrounding region. One person was killed and 19 wounded in the town of Irpin in the Kyiv region. Ballistic missiles struck the Ukrainian capital, killing one person.
RFE/RL correspondent Alex Raufoglu, citing Ukrainian sources, reported that Kyiv again received no warning from partners, in particular the United States, of the missile attack overnight. US Secretary of State Marco Rubio later told him he could not confirm the reports. "What happened last night, I don't know exactly," he said.