Fire appliances from Willowbank, St Kilda and Dunedin attended the blaze in Opoho Rd shortly after 12.30am yesterday.
The clubhouse and stored tennis nets were destroyed, and the southern region fire safety officer, Mike Cahill, of Invercargill, was investigating the scene yesterday.
"The fire appears to be suspicious and it is now a matter for police," Mr Cahill said.
It was too early to determine if accelerants were used.
Detective Neville Aitken, of the Dunedin CIB, said the fire appeared to be arson and he appealed for anyone with any information "to come forward".
Due to the high winds yesterday, the clubroom was bulldozed by the Dunedin City Council, he said.
Club secretary Sue Marshall said the news came as a blow for the club, which had undergone a surge in support after coming close to "folding" last year.
"We have about 24 members now, so it is a viable little club . . . but we will rise from the ashes again."
The club is believed to have started in the 1930s, with the clubrooms built in the 1970s.
Several old trophies were destroyed in the fire, Mrs Marshall said.
The clubhouse was insured and it was hoped a new building could be built before the end of the year.
"I was thinking of repainting the clubrooms this week. I am glad I didn't."
