More than 70 firefighters in 13 engines and support vehicles attended the blaze.
A Hampshire Fire and Rescue Service spokesman said: "We got called out at 5.09am and properties within 100m of the fire were evacuated. Nobody has been injured.
"The fire is at a garden and flower shop that sells fireworks, it's called The Flower Factory.
"The fire was contained within the business and we managed to protect other businesses in the area.
"Bitterne Road West is likely to be closed until around lunchtime.
"There were 13 engines and other support vehicles. The fire is not out but is under control and the operation is being scaled back."