The force confirmed that no arrests were made following the fixture, and thanked both clubs and the vast majority of supporters for staying at home.
Assistant Chief Constable Bernard Higgins said: “I’d like to thank the vast majority of fans from both clubs who took responsibility to prevent the spread of coronavirus by staying at home and not gathering at Celtic Park or anywhere else.
“Where small groups of people did gather, officers engaged and encouraged them to disperse and return home.”
It comes in stark contrast to scenes earlier this month, when thousands of Rangers fans breached lockdown rules to gather in the streets of Glasgow after their side were confirmed as Scottish Premiership champions.
There had been doubts over whether the game at Celtic Park would go ahead, with officials demanding cast-iron guarantees from both clubs.
On Friday, Justice Secretary Humza Yousaf confirmed the fixture would be played, telling reporters there had been “extensive engagement” between ministers, both teams, the SPFL and Police Scotland.
Chief Constable Bernard Higgins went on: “The clear message to all supporters as the football season continues over the coming weeks is to stay safe by staying at home and please do not gather in large groups.”
He added: “I’m grateful for the co-operation and support from all clubs and we will continue to work with them and the Scottish Government to ensure the season can be completed safely.”