The blaze at Wythenshawe Hall, which broke out at about 03:30 GMT, destroyed the roof and caused extensive damage to an upper floor.
Insp Luke Breakspear, of Greater Manchester Police, said the fire investigation was in its infancy.
More than 50 firefighters tackled the fire at the timber-framed Tudor hall, which was built in 1540.
Wythenshawe was home to the Tatton family for about 400 years. It was donated to local people in 1926 and was previously run as a museum and art gallery.
Peter Lamb, Incident Commander with Greater Manchester Fire and Rescue Service, said having a sprinkler system would have made a difference to quenching the fire.
"We recommend sprinklers in all buildings where possible - it did have an automatic fire alarm system and thankfully that gave us the early warning which got us here within minutes, whereas if it hadn't had that would have been in serious trouble," he said.
Paul Selby, vice-chair of the Friends of Wythenshawe Hall, said: "As a result of the amazing work of Greater Manchester Fire and Rescue Service the hall is safe - obviously it will need a new roof and some cosmetic work inside."
Source: Friends of Wythenshawe Hall
A fire that badly damaged a 16th Century hall in Manchester is "suspicious", police have said.