The blaze at the Bob Jones Community Hub in Blakenhall was started in the early hours of May 2 and has hampered plans to reopen the centre in the coming weeks.
Firefighters managed to control the spread but not before the electrics were left with serious damage.
A full investigation is now underway into what caused the blaze at the Bromley Street site but it is suspected to have been started deliberately.
Councillor Ian Brookfield, leader of Wolverhampton Council, said: "This was a mindless and dangerous act which could have put lives at risk, and we are working closely with police and the fire service as they investigate the circumstances behind it.
"The Bob Jones Hub is an important community facility that many people from across the city rely on. This fire could have deprived the community of its use for the long term and, unfortunately, it has delayed the full reopening of the building to its community groups and hundreds of gym users.
"The building and site have been made secure and discussions with the current contractor are underway about replacing the damaged equipment."
Essential gas meters and distribution paperwork were destroyed with the gas supply currently disconnected – meaning there's no heating or water at the venue.
The air conditioning condensing units and associated pipework, insulation and its electric cables have also been damaged and will need to be replaced.
And electrical services local to the area were also destroyed, meaning a new fuse board, wiring systems, lighting and power outlets are required.
The fire comes at a time when the Bob Jones Community Hub is undergoing essential renovation works prior to reopening – and the contractor's compound for storage was also damaged together with roofing materials.
West Midlands Police has been contacted for comment.