Monday night's Glasgow Cup U17 fixture at Firhill Park - the home of Partick Thistle - was the first meeting of the Old Firm since Rangers were relegated to the Third Division and around 6,000 people attended the match.
The kick-off was delayed as supporters set off flares and smoke bombs and damaged seats in the stands.
Fans also reportedly invaded the pitch and Police Scotland said three arrests were made at the game which Rangers won 3-2.
Two 17-year-old boys were arrested inside the ground over an alleged pitch invasion and a 19-year-old man was arrested outside the stadium in connection with a minor assault.
A report will be sent to the procurator fiscal and both clubs say they are helping police with their investigation.
A Celtic spokesman said on Tuesday: "We are looking into last night's match in more detail, together with all the relevant authorities, and clearly will deal with any issues appropriately."
A Rangers spokesman said: "It is disappointing that the off-field incidents at the Glasgow Cup Final last night detracted from a good game of football and a terrific result for the Rangers under-17 team.
"The club will assist the police with all their inquiries."