Police, paramedics and fire crews are said to be attending the incident in London Road, Hilsea.
Road closures are in place near the Coach and Horses pub.
Photos show a large fire in one of the flats with the balcony appearing to be well ablaze.
The images are from Paul Garrod.
A spokesman for Hampshire Constabulary said: ‘We were called at 3.46pm today (28 May) to assist fire service with traffic management in London Road following a fire at a block of flats.
‘We remain at the scene.’
In a post on Facebook, Portsmouth Police added: ‘Please be aware we are on scene along with Hampshire and Isle of Wight Fire and Rescue Service at a fire on the junction of London Road and Beechwood Road in Hilsea.
‘There are a number of road closures in the area that will affect you getting in and out of the city.
‘We will update you as soon as we have one to provide.
‘Thank you all for you patience and understanding at this time.’