The blaze started in the early hours of this morning and gutted much of the building and damaged the roof.
The buildings, which are used by Peterborough City football club and other organisations, have been largely destroyed by the attack.
A spokesman for Cambridgeshire Fire and Rescue told the Peterborough Telegraph: “At 4.17am on Monday (December 6) crews were called to a fire at Bretton Water Park in Peterborough.
“Crews from Stanground, Dogsthorpe, the Peterborough Volunteer Fire Brigade and Thorney, along with a turntable ladder from Cambridge and a water carrier from Ramsey, attended the incident.
Firefighters arrived to find a fire in a single-storey building used as changing facilities, which has spread to the roof.
“Wearing breathing apparatus they extinguished the fire using hose reels and a jet.
“The crews returned to their stations by 9.15am.
“The cause of the fire was deliberate. Anyone with information should contact police by visiting www.cambs.police.uk to submit an online report or call Crimestoppers on 0800 555111.”