Firefighters, police and the ambulance service all attended the blaze at Marytree House in Craigour Green, Moredun, at about 2:40am. Four people were treated by paramedics for slight smoke inhalation this morning.
A fire service spokesman said four fire engines and a specialist height appliance were sent to the high-rise building.
He said: “There were four casualties treated by the ambulance staff for slight smoke inhalation.”
The spokesman said that the fire was contained to the third floor landing area and that firefighters extinguished the flames and had left the scene shortly after 4am.
One eye-witness said that many residents spilled onto the street outside the multi-storey block.
And they said that police officers - both uniformed and plain clothes - were also in attendance.
A Police Scotland spokesperson said: “A 34 year old woman has been arrested in connection with wilful fire raising at a block of flats in Moredun.
“Emergency services were called to the property around 0240 on 22 March 2019, nobody was hurt in the incident.
“Enquiries are ongoing.
“During the response to this incident a small cultivation of cannabis plants, worth approximatley £1000 was discovered at a neighbouring flat.
“A 32 year old man was arrested and charged and a report will be sent to the Procurator Fiscal.”
Sign up to our newsletter: enter your email in the box at the top of this article to get daily updates straight to your inbox.