The inquisitive feline briefly brought play to a halt at the Vodafone Arena during the second half of Bayern's 3-1 win, before comically going on to win a man of the match poll held by the Bundesliga giant.
UEFA did not see the funny side, though, and Besiktas has been ordered to pay a hefty bill for what was deemed "insufficient organisation".
The fine also relates to the throwing of objects and stairways being blocked.
Bayern was also fined on Wednesday for a separate incident during their semi-final with Real Madrid – a human pitch invader and illicit banner leading to a €25,000 punishment.
Meanwhile, time-wasting by ball boys during Roma's clash with Shakhtar Donetsk earned the Serie A club a warning from UEFA, with the setting off and throwing of fireworks incurring a €7,000 fine.