Ten fire engines were deployed to deal with the fire, which ripped through a four-storey flat above the Tesco Express store by the entrance to the shopping complex.
Police are on the scene and all roads in the area that were closed have now been re-opened.
The shopping centre remains open to visitors, but the car park is closed.
None of the flat’s occupants were seriously injured, although three people are believed to have been treated for smoke inhalation.
The fire service was called to the scene at just before 1pm, and the building was evacuated.
Crowds gathered outside the building while firefighters fought the flames and the blaze was put out at around 2.30pm.
Deputy Chief Neil Odin of Hampshire Fire and Rescue Service said: ‘The flat is severely damaged. It has been absolutely gutted but luckily it was the only flat that was internally affected by the fire.
‘There are no serious injuries as a result of the incident but two people were subsequently treated for light smoke inhalation.
‘An investigation has now been launched into the cause of the fire which is not yet known at this stage.’
Appliances were in attendance at the incident from Cosham, Southsea, Havant, Fareham and Eastleigh.
Eyewitness Lyn Murphy was walking past the flat when she saw smoke coming out of it. She said: ‘It was just a bit of smoke at first but then there was a lot of it.
‘I could see flames in the flat.’
A South Central Ambulance Service spokeswoman said they were called at 1.20pm and treated a patient, although they did not require hospital treatment.
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