Minor damage was caused from the fire which was lit underneath the wooden pirate ship, a Hastings District Council spokeswoman said.
The council estimated the cost of the attack to be about $3000 which included damage to the timber structure, a climbing rope and artificial turf.
Police and the fire service were continuing to investigate the incident.
Hastings district councillor Sandra Hazlehurst said it was very disappointing after all the hard work put in by the Hastings Host Lions Club and council to complete the new play area, which was officially opened on November 29.
"We have zero tolerance for vandalism," she said. "We are in the middle of setting up neighbourhood support groups in the Mayfair area so there will be eyes and ears on what is happening in the park. The community is absolutely loving the playground and we're not going to allow a few troublemakers to ruin it for us."
The pirate ship was expected to re-open Friday afternoon.