Several of the French club's supporters were taken to hospital with knife wounds, while others were treated for minor injuries after they burnt the Ukrainian flag, the local Hromadske television station reported.
Several Dnipro fans were detained by police, it said.
Dnipro reached the last 32 as Group F runners-up, five points behind Inter Milan, with seven points from six games.
"There was a fight between the French and Ukrainian supporters at Prorizna Street in Kiev," an eyewitness was quoted as saying on www.hromadske.tv.
"There were a lot of wounded people, with knife cuts and bruises from bats. I also heard at least 10-12 gunshots."
Anton Gerashchenko, advisor to the Ukrainian Ministry of Internal Affairs, said in a statement on his Facebook page: "Two French fans were hospitalized with head injuries.
"Those French supporters inopportunely were caught in the heat of the moment. And our hooligans will be accusing the French men, no matter who started the fight."
Earlier this season Dnipro fans attacked supporters of Danish club FC Copenhagen in a Champions League qualifier.
In July UEFA ordered Dnipro to play matches in Kiev -- 220 miles (354 km) to the north west -- amid safety conrcerns over staging matches in the conflict-torn east of Ukraine.
(Reporting By Igor Nitsak, Editing by Tom Hayward)
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