Three crews - one from Horsham and two from Crawley - were called to the MFA Bowl centre, in Albion Way, at about 7.30am.
The fire service said smoke was seen issuing out of the lower ground boiler room of the 30m by 40m building when firefighters arrived.
After further inspection it was discovered an electrical fire had broken out in the store room.
The electricity was isolated and the flames were extinguished using four breathing apparatus, two hose reels and a water jet, the fire service added.
No-one was injured and crews remained at the scene until 9.40am ventilating the building.
The fire is believed to have started accidently.