Crews tackled the blaze at The Ranch, which opened in Southmead in 1955, at about 21:00 BST on Monday.
BBC Radio Bristol reported local residents cried in the street as the adventure playground in Doncaster Road was engulfed by flames.
Avon Fire and Rescue said the fire was under control by about 21:50 BST.
Learning Partnership West (LPW), which manages the playground, said the community has been "robbed of an important facility" which had given "so much enjoyment over five decades".
John Savage, from LPW, said it was a "terrible event for the children and young people of Southmead".
He said: "I'd like to reassure the people of Southmead that LPW will rebuild the adventure playground as quickly as we possibly can.
"However, we hope to run play sessions and other activities from the site, where our other building has been left unaffected, as soon as the police and fire service allow us."
He said it was "particularly hard to take" after LPW and volunteers had renovated the play area earlier this year.
Neighbourhood inspector Mark Runacres, from Avon and Somerset Police, said it was a "sad day for the community" and asked anyone with information to get in touch.
The playground featured climbing walls, an outdoor classroom and a zip wire.
A fire that badly damaged a children's playground in Bristol was started deliberately, the fire service has said.