Fire crews attended the blaze at a block of flats on Westfield Road, Edinburgh, at around 12.30am this morning.
A Police Scotland spokeswoman said: "It appears it was a possible fire started deliberately.
"Four people were taken to hospital as a precaution with some minor smoke inhalation.
"The fire originated in the common stair of the block, which has 16 flats in the property."
A Fire Scotland spokeswoman said: "Crews from Sighthill and Tollcross attended a fire in a cupboard in a common stair in a block of flats.
"We used one high-pressure hosereel and two firefighters with breathing apparatus to extinguish the fire, and a further firefighters with breathing apparatus for search and rescue.
"Three females and one male were taken to Edinburgh Royal Infirmary suffering slight smoke inhalation."
A Police Scotland spokesman added: "Fortunately, no-one was seriously injured as a result of this incident and officers are now conducting local inquiries to identify whoever was responsible for starting the fire.
"Anyone who remembers seeing anything suspicious in the Westfield Road area in the early hours of Sunday morning should contact police immediately.
"Similarly, anyone with any further information relevant to this investigation is also asked to get in touch."