Zookeepers said Qabid had gotten wedged in the swing before, but had previously been able to free himself without help.
Scottish Fire and Rescue Service Group Manager John Hanlin said the rhino had to be sedated during the rescue.
"Our crew used specialist cutting equipment which is normally used for the extraction of persons involved in road traffic collisions," he said.
"Once the firefighters managed to cut the tire and free Qabid, the zoo vets gave him a drug to counteract the sedative and bring him round -- and he was quickly back to his mischievous self," Hanlin said.
The zoo thanked the firefighters for their help.
"Our greater one horned rhino Qabid loves to play with his tire, it's one of his favorite things to do," said Darren McGarry, head of living collections at the Edinburgh Zoo.
"On Sunday, he managed to get his head and a leg stuck while playing and we had to contact the Scottish Fire and Rescue Service for assistance to use their specialist cutting equipment," he said. "The tire was safely removed and Qabid is doing fine. We would like to thank the firefighters for their help."