Hospital officials said the man's injuries were not serious.
Authorities on Wednesday also announced the arrest of a 27-year-old English man accused of selling 28 forged tickets for EUR58,000 (US$78,000) for Wednesday night's final between AC Milan and Liverpool.
The incidents were reported amid massive security, with 8,500 police deployed at the Olympic Stadium, city center and airport and another 6,500 in a support role.
Police reported no other trouble among tens of thousands of English and Italian fans in central Athens.
In the port town of Rafina, near Athens, an English fan told police a taxi driver drove off with his luggage and match ticket after he refused to pay EUR95 (US$125) for a ride that should cost less than EUR25 (US$33).
Turkey has found itself in a circle of countries subject to US and European sanctions. Are they dangerous for Ankara? What is Turkey going to do in response?