Firefighters attended the scene in Hampden Park Drive after a call came in at 5.32am, on Friday August 15.
Two appliances from Eastbourne and a specialist support unit from Lewes were used to battle the blaze, and firefighters stayed at the scene until 6.44am.
Match secretary of the bowls club Bob Depper said firefighters faced a 'devastating' blaze.
Bob said, "The clubhouse had been set ablaze after a burglary.
"The burglars had sawn through the outer skin of the clubhouse and run amok before setting fire to it."
Mr Depper said the clubhouse has been made safe, however the whole bowls area cannot be used due to health and safety precautions, although the greens are unaffected.
The incident has happened just weeks after vandals smashed the windows of Lakeside Tea Chalet's disabled toilet and damaged the door of a rugby club in Hampden Park.
PC Dave Selby, a neighbourhood support officer for Hampden Park, said the park has been identified as an area where youths congregate and drink.
It is patrolled by both the normal PCSO vehicle patrols and by Operation Blitz — method to tackle antisocial behaviour by youths and youth crime.
The Friends of the Hampden Park, together with representatives of all the sports clubs and businesses based in and surrounding the park, formed a focus group this year to pool their information.
Chairman of the Friends Sandy Boyce-Sharpe said, "It is very demoralising for anyone trying to run a business or a sports club in the park to suffer this (vandalism] continually."
As a result of the incident and the extensive damage to the pavilion area of the bowls club, its bowls programme has been rescheduled.
Mr Depper said, "The immediate bowls programme of both Hampden Park Men's and Ladies' Clubs has been rescheduled for the foreseeable future. All match commitments will be met.
"Hampden Park Bowls Association, Men's and Ladies' Clubs wish to thank all the clubs that have offered their help and support."
Anybody with any information is asked to contact Eastbourne CID on 0845 60 70 999 quoting serial 269 of 15/08/08 or alternatively, contact Crimestoppers free on 0800 555 111.