The fight broke out at Harton Primary School, in South Shields, South Tyneside, before the children – aged five to 11 – took the stage.
Other parents in the audience intervened and pulled the two dads apart. A spokesman for the school said that the incident was not witnessed by any of the children, who were preparing for the play backstage.
A 39-year-old man was arrested on suspicion of assault and bailed, while the 32-year-old victim was taken to hospital for treatment.
It is believed that surgeons were able to reattach his finger.
One witness told reporters: “We were all waiting in a room for the show to start. I’d got there early to make sure I got a good seat.
“I heard a bit of noise from the back of the room and looked around to see what was happening. A man in a white hat stormed in and went for another dad.
“They were fighting and blood was flying. I didn’t see it, but I heard that a finger was bitten off.
“The fight was broken up by teachers quite quickly and the man in the hat disappeared.”
A spokesman for the school stated: “We are assisting the police with their enquiries and can confirm that the incident was not witnessed by any of the children, nor were they at risk at any time.”