Fans were involved in what police have described as "shameful" clashes on the pitch after Celtic knocked Rangers out of the Scottish Cup on penalties.
Some Celtic fans ran on to the field at the final whistle to celebrate after their team secured a 4-2 win in the shootout, and a place in the competition's semi-finals, after a goalless draw.
Hundreds of Rangers supporters also ran on to the pitch at the end of the Old Firm derby.
Missiles were thrown, and there were some skirmishes, before order was restored by police and stewards, who formed a barrier between the two sets of supporters.
Celtic's team, backed by 7,500 fans at one end of the stadium, had not registered a shot on target during 120 minutes of action in Glasgow.
Police Scotland officers, along with stewards, were faced with "extreme hostility and violence", according to Chief Superintendent Kate Stephen.
CS Stephen said: "The behaviour of a number of supporters at the Scottish Cup quarter-final between Rangers and Celtic at Ibrox today was shameful.
"It must be condemned by everyone involved in football and wider society.
"A number of arrests have already been made, and Police Scotland will now work with both clubs and the Scottish Football Association to carry out a robust investigation following the scenes on the pitch at the conclusion of the match.
"Officers and stewards were faced with extreme hostility and violence over a sustained period, with many individuals having armed themselves with items clearly intended to cause harm.
"Officers and members of the public have been injured in this despicable display, and I want to express my thanks to all officers and staff deployed."
CS Stephen added that some supporters had gained entry to Ibrox without tickets.
She added: "The investigation will also include the actions of some supporters who entered the Broomloan Road stand without tickets before the match started, forcing delays in the security operation and the turnstiles to be closed for a period of time."
The Scottish Football Association also condemned the pitch invasion.
A statement read: "The Scottish FA condemns the behaviour from supporters entering the field of play following today's Scottish Gas Scottish Cup Quarter-Final at Ibrox Stadium.
"An investigation will be carried out immediately in line with the Judicial Panel Protocol."
There was "some sort of fracas" between a spectator and a member of Celtic's backroom team, according to Martin O'Neill.
Asked about the incident, Celtic's manager said: "As we were making our way back, I think there was some sort of fracas. Somebody tried to get on the field. I don't know, all I saw was there was a bit of a scrum down at the bottom.
"The security men, in fairness to them, were wanting to get people off. But there is a natural euphoria about winning a game, and about fans joining in. If this has gone too far, that would be disappointing."
Rangers head coach Danny Rohl said that he did not see the pitch invasion.
Rohl said: "I was not on the pitch in the moment, I did not see it until now. I think we all know the emotional situation after a game. Nobody likes to see this.
"It was a great atmosphere for 120 minutes, and should be like this. The other things should not be in the stadium - or in football."
(c) Sky News 2026: Rangers and Celtic fans in 'shameful' clashes on pitch after Scottish Cup tie
Fire shuts Scotland's busiest train station for at least two days
Police appeal for help to identify man found dead in a wetsuit
Cancer death rates fall to historic low - as types with biggest drop in fatalities revealed
Diane Sindall: Family of murder victim appeal for information after wrongful conviction
Spend more on defence or risk being vulnerable to missile and drone attacks, UK warned
Lib Dem leader calls for King's US state visit to be cancelled after Trump's criticism of Starmer
The 'dropping tax band' trick that could boost your pension | Money newsletter
Gender-affirming hormone treatment for teenagers halted by NHS
Two drivers dead after four-vehicle collision near Bristol
