Around 7000 supporters turned out for the under-17s match last night and police reinforcements moved in to restore order among sections of the crowd.
Three men were arrested and CCTV footage is being reviewed in a bid to trace people responsible for the disorder.
Officers said an inquiry into incidents of disorder has been launched and any witnesses are asked to come forward.
A spokeswoman said: “Three people were arrested and several pyrotechnics were let off.
“Inquiries are continuing to trace those responsible.”
Witnesses said thugs paid no attention to the game, and stood with their backs to the game as they shouted at their rivals.
Flares and smoke bombs were set off during the Glasgow Cup Final at Parkhead.
Uniformed officers rushed in to the stand the control the trouble during the youth fixture.
It comes after the Evening Times revealed under-20 fixtures between the Old Firm clubs would be played behind closed doors this season.
The match, which saw Celtic lift the tophy with a 1-0 win, prompted outbursts of violence.
However, the disorder was contained by a strong police presence, as the crowd celebrated Aidan Nesbitt’s second half goal.
Some fans, with scarves over their faces, tried to break through segregated areas after shouting sectarian abuse.
A smoke bomb was set off by Celtic fans while Rangers fans threw flares and firecrackers.
Witnesses said sections of the crowd on both sides spent the first half an hour taunting each other.
Before the match started, police were brought in to keep the rival fans apart.
Rangers supporters were walked along London Road with a large police presence to prevent any pre-match clashes.
Crowd trouble also marred the last meeting between the clubs at this level a year ago
Arrests were made as seats were ripped up and pyrotechnics used at Firhill, the home of Partick Thistle, as Rangers won the cup.