The theft occurred during a league match between Sporting Lisbon and Vitoria Guimaraes on Saturday, but was not reported to police until the following day.
"Several individuals wearing balaclavas forced open a gate" in the garage of the stadium, where the tournament's showpiece will be played on May 24th, the police said in a statement.
In addition to the trophy, other items of equipment belonging to UEFA were also taken.
These items, along with the trophy, have since been returned to European football's governing body, a police spokesman told AFP.
Thirteen suspects have been identified, according to a police statement, which gave no details of the operation that led to the recovery of the stolen items.
The investigation is ongoing and the police said they expect to recover more items and make further arrests in the coming days.