The fight, involving 40 English fans and more than 20 Ukrainians, broke out after the two sides traded insults, police said.
"Three British citizens ... were taken to hospital with wounds to the head and hands. After getting medical treatment they were taken back to their accommodation," it said.
Local media reported that the Ukrainians were hooded and armed with knives and bottles, and that there had been no arrests so far.
The injured England fans were taken to hospital, treated and driven back to their hotels, the reports added.
England top Group H with 15 points, ahead of Montenegro on goal difference. Ukraine sit third with 14 points.