Cosham Fire Station were called to the scene offÂ Woofferton Road, Paulsgrove, at 6.30am.
Crew manager Simon Bone said: '˜The fire had already spread when we got there.
'˜We believe it was caused by an electrical fault with the vehicle.'
Firefighters put the blaze out within 20 minutes, after six people called the fire service to report the incident.
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Mr Bone added: '˜Luckily it didn't cause too much damage, it was mainly just external damage to the shed.'
He confirmed the shed belonged to the same person as the van in which the fire started.
The fire crew left the scene just after 7am.