Emergency services were called out to Torrance Park, Drum Brae, shortly before midnight yesterday.
A probe has now been launched into the cause of the fire and officers have made an appeal for information.
A man and a woman were checked over by crews at the scene, while residents living in the same block were advised to remain in their homes until the smoke had cleared.
Firefighters wearing breathing apparatus used a high pressure hose reel to extinguish the blaze.
A Police Scotland spokesman said: “The incident occurred yesterday at around 11.45pm when a fire within a stairwell was reported to police and emergency services.
“Police attended along with the Scottish Fire and Rescue Service and the fire was extinguished quickly.
“Officers believe the fire is suspicious and are appealing for information.”
Inspector Liz Duthie added: “Thankfully no one was injured as a result of this fire, nevertheless we are treating it as suspicious.
“We are also conducting additional patrols in the area in order to provide community reassurance.
“Anyone with information regarding this incident, or who saw anything suspicious last night, is asked to contact police immediately.”
Those with information can contact Police Scotland on 101 or anonymously through Crimestoppers 0800 555 111.