Around 30 hooded Ukrainians armed with knives brawled with England supporters in a coffee shop, the Komsomolskaya Pravda reported.
The attackers then fled, and no one has been arrested.
Three of the England fans were taken to hospital – one with a stab wound, one with a head injury, and a third with severe bruising. It is understood all three have been released from hospital and have decided no to help the police with their investigation.
Amateur video showed one of the injured men lying on the pavement with other people attending to him while police and ambulances arrived.
The Foreign Office said: "We are aware of incidents in Kiev involving British nationals. We are providing consular assistance."
England will take on their Ukrainian opponents in Kiev's Olympic Stadium on Tuesday night.
A win for England would move them to within touching distance of a place in next summer's finals in Brazil.
The British police delegation in Kiev for the match warned fans to be cautious in the city before and after the game.
Rachel Barber, head of the UK police delegation, said:
"We are aware of what happened last night and we will be going round most of the major bars, including this particular one, to make sure there are no problems."
"We would urge supporters to enjoy themselves but to do so without upsetting anybody."
"I am pleased to say that currently the atmosphere in the town is good, so in that sense what happened last night was out of the blue."
"Sometimes there can be an element of bravado on social media and you can never legislate for something happening but hopefully the England fans will just have a good time in what is a fantastic city."
Source: Sky News