Five football fans were injured during a "dreadful" crush before Sunday's Old Firm game.
Police said one person was taken to hospital after falling from a wall, while four others were treated by first aiders at the scene before attending the match.
Celtic fan Mike Robb posted a "frightening" picture of the crush on Twitter, saying it was "really dangerous" and that there were "no police or stewards in site".
Another match goer, Jamie Kerr, posted: "Absolute chaos at Celtic Park. People being crushed. Turnstiles not open. Police not in control. Kids crying. Dreadful."
Police Scotland and Celtic have launched an investigation into the incident.
Ch Supt Brian McInulty said: "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."
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."
Celtic supporter liaison officer John Paul Taylor posted on Twitter: "Apologies to fans affected by overcrowding issue at North Stand earlier, the Club will be investigating the cause to ensure no recurrence."
Celtic won the game 1-0 as manager Brendan Rodgers came up against Rangers boss Steven Gerrard, who played under Rodgers at Liverpool.
Additional reporting by Press Association.
