The blaze in Woodville Road took place last night (Friday, September 16), Boston Borough Council has said.
As a result of the fire, the gates to the park have been locked.
"The play area remains closed until arrangements are made to remove the damaged equipment and make the area safe,” the council said in a statement on its Facebook page.
The pirate ship was opened in October 2019.
The equipment – which reportedly cost £15,000 – was jointly funded by Boston Big Local and Boston Town Area Committee.