Lincolnshire Police were alerted to the fire at the play area in Woodville Road at about 9.30pm on Friday, September 16.
The outbreak destroyed a pirate ship play feature installed in 2019 at a cost of about £32,000.
No arrests have been made, the force said.
The park is owned by Boston Borough Council.
On Saturday, the authority said the area would remain closed to the public until the damaged equipment had been removed and the area made safe.
Today, leader of Boston Borough Council Coun Paul Skinner, said: “It is extremely disappointing that anyone would commit such a mindless and needless act of vandalism to a popular piece of play equipment which was funded by Boston Big Local and was used by the children in our community.
“These actions have meant that certain parts of the park are now out of use. I urge anyone with any information to come forward and help the police with their investigations.”
Anyone who may have witnessed anyone acting suspiciously or witnessed the incident taking place is asked to call Lincolnshire Police on 101 quoting reference 22000541413.
The force would also like to hear from anyone who may have CCTV or dashcam footage of the area.