Five people have been injured trying to get into Sunday’s Old Firm game at Celtic Park.
One was taken to hospital after falling from a wall and others were treated at the scene before going into the match.
Celtic fans said some supporters were forced to climb over a high fence to escape a crush, which they claim was caused by the stadium entry points being changed.
Police and Celtic FC said they would be reviewing their procedures.
One supporter, who did not wish to be named, told the BBC Scotland news website: “People couldn’t walk round the stadium anymore so there was a bottleneck under the north stand.
“Suddenly there was an absolute crush because there were about 1,000 people trying to get one way and about 1,000 trying to go the other way. The corridor is only 6-7 people wide.
“They kept letting people through from either side of the corridor and it became a crush, with people getting semi-trampled.
“I was behind a woman with a boy of about 10 who was getting rocked and people were panicking and climbing over the fences as they couldn’t actually breathe properly. It was that bad.”
He added: “Myself and my friends were fine but there were women and kids there. It must’ve been really scary for them.”
The Celtic fan said it took him 30-40 minutes to move 300 yards but that the police and club eventually stopped people going in so the situation resolved itself.
“It was an absolute joke,” he said. “The people at fault are the police for shutting the access and Celtic for not thinking about how the people flow would go.”
Ch Supt Brian McInulty, of Police Scotland, said: “Five people were treated by first aiders when fans were attempting to get into the stadium in the lead up to kick-off at Janefield Street.
“Four people were treated at the scene and then went into the ground, and the other was taken to hospital after a fall from the wall bordering Janefield Street.
“This was a dynamic situation, occurring 10 minutes before the match started.
“Officers and stewards reacted quickly upon realising there was an issue and put in place measures to relieve the congestion. This included putting in place cordons to prevent further entry at Janefield St and opening up London Road to allow fans to access the stadium from the south.”
He added: “We work closely with Celtic Football Club to ensure the safety of all fans attending matches. We plan and practice various scenarios to ensure that if an incident occurs it will be dealt with as quickly as possible, as happened in this case.
“We will review today’s incident and work with Celtic to ensure any learning is quickly put in place.”
A statement from Celtic Football Club said: “We are aware of the issues caused by congestion prior to kick-off. We are pleased that stewards and police were able to assist quickly and we thank our supporters for their patience shown while the matter was being dealt with.
“We will work closely with police to investigate and review this matter. The safety of our supporters will always be our priority.”
The final score was Celtic 1-0 Rangers.