Emergency services were called to the four-storey block of flats at St Catherine's Square in Perth at around 11.25pm on Tuesday.
The 26-year-old had jumped from the window by the time they arrived and was taken to Ninewells Hospital in Dundee.
A number of people were evacuated from neighbouring flats while firefighters tackled the blaze, and fire crews remained at the scene until 2.15am.
The Scottish Fire and Rescue Service (SFRS) and Police Scotland will carry out a joint investigation.
SFRS incident commander Billy McLintock said: "I would like to give my thanks to the firefighters and partner agencies for their swift and effective actions, which brought this fire to a safe conclusion."