The Kharkiv police department said six others were hurt, yesterday although the extent of their injuries remained unclear.
But local police spokesman Yaroslav Trakalo told the Ukrainska Pravda news site that two women's condition was "very serious".
The police statement said the female driver of the SUV vehicle had been detained, adding that a criminal case involving driving safety violations had been launched.
The charge carries a maximum sentence of 10 years in jail, the police statement said.
Kharkiv is located less than 300 kilometres northwest of Ukraine's eastern war zone in which more than 10,000 have died in fighting between government soldiers and Russian-backed insurgents.
The city itself was briefly the site of pro-Russian protests after Ukraine toppled its Kremlin-backed leadership in a February 2014 revolt.
But the city of about 1.4 million people has avoided being dragged into the conflict and remains firmly under the Ukrainian government's control.
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