Firefighters from Sprowston and Earlham tackled the fire at the former King Edward VII pub site which is undergoing a £1m revamp by the East Anglian Bangladeshi Islamic Trust.
Police remained at the site on Monday morning and confirmed the fire was the result of an arson attack.
A police spokesman said: “A man was seen to start a fire in an outbuilding before leaving the area.
“Norfolk Fire and Rescue Service attended and damage was caused to the outbuilding only.
“Police are investigating the incident and reviewing CCTV and would be keen to hear from anyone who may have witnessed the incident or has information concerning it.”
Planning permission was granted for the mosque at the former pub in December 2017 but the site had remained boarded up until recent months when work got underway on the redevelopment.
A new mosque is needed to accommodate the East Anglian Islamic Centre’s growing congregation of 250 people which is currently based on Rose Lane.
Outlining its plans the trust said that the former pub, which was built in 1902, would not be demolished. Instead, it will be refurbished and turned into a cafe for people to use regardless of their religious background.
Once finished the mosque will include a prayer hall, kitchen and cloakrooms on the first floor. Meanwhile the ground floor will house a counselling room, a gymnasium, prayer room, funeral room and office.
The site, between Waterloo Park Avenue and Edmund Bacon Court, will also have 20 parking spaces with a further 50 spaces available to the nearby St Luke’s Church.
When the plans were first made public, a spokesman for the trust said people living around the proposed site had been “very welcoming”.