The violence late Tuesday cast a fresh spotlight on concerns for fans' safety in Kiev as the Ukrainian capital prepares to host the 2018 Champions League final.
A police statement said two Turkish fans were stabbed while eight suffered less serious injuries during clashes that began on Kiev's main avenue Khreshchatyk before the game and lasted for nine hours.
The match ended with Dinamo thrashing their rivals 6-0.
The result means that the Turks progress to the Europa League as third-place finishers in Group B while Kiev finish bottom of the group and are out of the competition despite the win.
A spokeswoman for the Kiev mayor's office said that eight of the Besiktas fans had been released from hospital by Wednesday while two more needed more time to recover. Dinamo fans were seen burning a Besiktas flag
One of those injured underwent surgery while the other still needed to convalesce, the spokeswoman said.
There was no immediate response to the incident from the European football's governing body EUFA.
Besiktas and Dinamo are both known to have passionate supporters that include some ultra-nationalist groups.
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