The cost of repairing the damage to the will run into several thousands of pounds.
It is believed that fuel was poured on to equipment and then set alight, damaging the slide unit and a large section of the flooring.
The toddlers’ play area has only been open a couple of years and cost more than £80,000.
One neighbour said that the fire was at about 7pm on Bank Holiday Monday. Fire crews parked in the entrance lane to the park, from where they ran a hose to extinguish the blaze.
The playground has been sealed off and a sign on the gate warns people not to enter for health and safety reasons.
The rest of the park remains open.
Cllr Michael Bell (Labour) who represents Rodway ward on South Gloucestershire Council, said: “This is just mindless vandalism. Local children have now been deprived of using the play equipment whist repairs are taken out.
“We are now in the summer period when the nights are longer and warmer, and what should be evenings full of fun and exercise for our young residents in Springfield Park, has now been denied them.
“Also South Gloucestershire Council will have to find at least £8,000 to cover the cost of replacing the damaged equipment.”
A South Gloucestershire Council spokesperson said: “Unfortunately we had to close off the play area in Springfield Park due to vandalism that took place on Bank Holiday Monday.
“We are currently speaking with suppliers to replace the damaged play equipment and hope to have the area fully open in time for the summer school holidays.”
Springfield Park in Mangotsfield was one of the outdoor spaces in South Gloucestershire protected as a Queen Elizabeth II Field to mark the Queen’s Diamond Jubilee.