Fire crews were called to the Laura Ashley store at the Montague Centre in Worthing at 12.20am today (Saturday, October 6), a spokesman confirmed.
Bedding belonging to a rough sleeper is believed to have been intentionally set fire to, the fire spokesman said.
The fire spread to the ground floor of the three storey building, according to the spokesman.
Crews used four breathing apparatus and one hose reel to extinguish the flames, which were out by 12.35am, the spokesman said.
The fire service left the scene at 2.02am.
Police were also called to the scene.
This morning Graham Sawyer, who has been sleeping rough outside the Laura Ashley store for some time, said he was busking round the corner when someone alerted him to the fire.
His guitar, which he is often seen playing in the town centre, was undamaged, as was some of his bedding, and he said he had been donated some new quilts since the fire.
Julie Pellegrino, assistant manager at Laura Ashley said staff were alerted at 2am.
She said the fire had left part of the store 'smelly and mucky' and said: "There is quite a bit of water damage and one of our room sets has been burnt."
She said the window was shattered and one of the sofas had caught fire.
"We will not be opening today or tomorrow, we will have to see about Monday," she said.
"We hope to be open in some form on Monday."