The furniture had been left in the street but the force say it is not yet clear how it started.
An investigation has been launched to find out if it was deliberate.
Police Scotland sergeant Paul McIlravey said: “Thankfully no one was injured and the fire was put out by the Scottish Fire and Rescue Service.
“The fire resulted in damage to several flats and the communal roof.
“It is currently unknown how the fire was started and we are keen to speak to anyone who saw anything suspicious in the area at the time.
“Anyone who can help is asked to contact Police Scotland on 101, quoting incident number 2839 of Wednesday, 25 August, 2021, or make a call anonymously to the charity Crimestoppers on 0800 555 111.”
Neighbours were forced to exit out of the rear of the address as flames soared into the air just outside the main entrance.
Fire crews from Macalpine Road and Blackness Road assisted in tackling the blaze before standing down at around 7.38pm.
Fire which forced evacuation of Dundee flats started in ‘pile of furniture’