Around six to eight youths were seen running away after setting light to an old television set they had taken to Wisbech bandstand.
Fire crews were called to the fire last night (Thursday) and an eye witness said he saw the group fleeing the scene just as fire crews arrived.
The fire seems to have been started in the middle of the bandstand but it is not known yet what the extent of the damage will be.
A spokesman for Cambridgeshire Fire & Rescue said: "On Thursday (31) at 6.13pm one crew from Wisbech was called to a fire in the open on Lynn Road, Wisbech.
"Firefighters arrived to find a small fire in a bandstand."
The spokesman said: "Using a hose reel and small gear, the fire was extinguished before the crew returned to their station by 6.55pm.
"The cause of the fire was deliberate."
The threat to the bandstand comes after it was used throughout the summer for a popular series of free concerts and with a Christmas special being planned.
Around £30,000 was spent last year on refurbishing the bandstand and a group calling themselves Friends of Wisbech Bandstand has been instrumental in bringing events to the park.
A local businessman said the same youths seen running from the scene were later witnessed breaking pumpkins outside people's homes along Norwich Road.
He said he had spoken to police about the incident.
One person confirmed on a local Facebook group that it was TV set that had been set alight.
"Luckily there was only minimal damage to the bandstand," she wrote.
Anyone with information should contact police by visiting www.cambs.police.uk to submit an online report or call Crimestoppers on 0800 555111."
A Fenland Council spokesman said: "There was a small fire underneath the floor of Wisbech band stand.
"Upon inspection the damage wasn't as bad as initially feared, as it was some scorch marks to the tiles."
The spokesman added: "We've tidied the site today and work is being planned to replace the scorched tiles."
A police spokesperson said: "Last night a dispersal order was put in place around Wisbech to disrupt antisocial behaviour. The order was enforced by local officers and supported by the Community Action Team.
"Officers have increased patrols in the area and longer-term enforcement action is underway to tackle those responsible."
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