Police said missiles were thrown at officers during violent scenes in the city ahead of the final on Sunday.
There were also reports of broken windows and that officers would use stop and search powers to "prevent disorder and serious violence."
Celtic celebrate after winning their penalty shootout at Hampden. (AP PHOTO)
Videos shared on social media appeared to show flares let off in Glasgow city centre and gangs of masked people running through the streets. Some shoppers could be seen taking cover in a store entrance as people charged past.
"We have dealt with a number of incidents in Glasgow city centre today involving individuals engaging in disorder and violence across the city," chief superintendent Stevie Dolan said in a statement.
"The use of weapons or violence will not be tolerated and officers will take action where necessary to ensure safety.
In the game itself, a goalless extra period was followed by a shootout with Rangers' Ridvan Yilmaz seeing his effort saved by Kasper Schmeichel before Daizen Maeda secured the win for Celtic.
The match kick-off had been briefly delayed due to flares in the stadium, with Nedim Bajrami putting Rangers ahead four minutes before the break, capitalising on a rebound to slot into an empty net.
But Celtic took control in the second half as Greg Taylor's deflected shot wrong-footed goalkeeper Jack Butland in the 56th minute before Maeda put the Premiership leaders ahead with a composed finish inside the box four minutes later.
Mohamed Diomande equalised for Rangers with another deflected shot in the 75th before Nicolas Kuhn scored and thought he had won it for Celtic three minutes from time.
But Danilo headed in another Rangers equaliser about 20 seconds after the restart to send the match to extra time.
With AP
