The Glasgow Cup under-17s fixture at Celtic Park on Monday night was attended by a crowd of about 8000 and, with the senior teams playing in different leagues, it was the highest-profile meeting between the Old Firm this year.
Groups of fans were escorted to the stadium in the east end of Glasgow by police and the match, which Celtic won 1-0, was disrupted by flares and smoke bombs.
Arrests were made by officers for possession of a bottle, which is not permitted inside stadiums, a fireworks offence and an alleged breach of the peace.
A police spokeswoman said: "There were three arrests in total, one within the ground for possession of a controlled container, one before the game for contravention of the Fireworks Act and one after the game for an alleged breach of the peace.
"Several pyrotechnics were let off during the game and inquiries are continuing to trace those responsible."
It follows similar scenes at the same match last April when the under-17s sides played at Firhill, the home of Partick Thistle. At that game, the kick-off was delayed as supporters set off flares and smoke bombs, and damaged seats in the stands.
Two fans were arrested for invading the pitch and further arrests were made in the weeks after the match.