The fire took place this evening in the part of the building used by the Cathedral Archer Project homelessness charity.
A message on the Cathedral's Facebook page said no one was hurt in the incident but that the cause was being investigated by the fire service.
A cathedral spokesperson said: “We do not yet know the full extent of the damage but the fire is out.
“It is particularly sad and difficult as the fire has affected the part of the Cathedral where the Cathedral Archer Project work from and meet the needs of some of the most vulnerable people in our City.
“No one was hurt in the incident. The cause of the fire is being investigated by South Yorkshire Police and the Fire and Rescue Service.”
More to follow.