The early morning blaze in Chapman Street, in the south side of Glasgow, is being treated as wilful fire setting, according to the Scottish Fire and Rescue Service.
Crews were called to the address at 6am and evacuated residents, including two adults and a child who were rescued from a first-floor flat using a ladder.
Twelve people were treated by paramedics at the scene but none were taken to hospital.
A fire service spokesman said: "We arrived and were immediately faced with a well-developed fire within the storage cupboard in the common close.
"There was heavy smoke logging within the close, affecting the means of escape for the residents.
"They quickly extinguished the fire using a high pressure water jet and assisted those residents who had self-evacuated."
Anyone with information about the fire is asked to contact Police Scotland on 101 or Crimestoppers anonymously by calling 0800 555 111.