Several incidents occurred before and during the Champions League match between AEK and Ajax on Tuesday, Sky Sports reported.
Most injuries are believed to not be serious, although one officer was kept in hospital overnight.
A statement from the police said the officers were "injured by thrown bottles and other objects."
Greek riot police intervened at the beginning of the match following clashes between the Ajax and AEK fans.
Police were seen hitting fans of the Dutch side, leaving some of them injured. AEK fans were also seen throwing flares into the stands housing the Ajax fans.
In the second half, firecrackers were set off, with players from both sides pictured rubbing their eyes as the smoke drifted across the pitch.
Earlier in the day, police had clashed with Greek fans in Athens. Supporters of rival Greek clubs were involved in violence in the city, while youths throwing petrol bombs caused traffic to be blocked.
Ajax won the match 2-0 to qualify for the last 16 of the Champions League for the first time in 12 years.
AEK already faces a UEFA punishment for raising ticket prices for Bayern Munich fans for a Champions League game in October.