According to an eye-witness, the roof was 'coming off' at the Argos store and the traffic lights outside were 'blown over'.
The Sainsbury's entrance porch roof has also reportedly collapsed. The side door is said to be in use for entry and exit.
Pictures also show structural damage to a property in nearby Eaton Court.
West Sussex Fire and Rescue Service (WSFRS) confirmed crews were called at 12.30pm to 'reports of loose cladding' on the Argos building at Lyons Farm in Sompting Road.
A spokesperson added: “Joint Fire Control mobilised a crew from Worthing Fire Station to the scene where they worked with police to put a cordon in place to keep people safe.
“With the bad weather expected to continue this afternoon, WSFRS is urging people not to travel and to stay indoors where possible to avoid putting themselves in danger.
“If your journey is unavoidable, please take extra care when out on the roads. If you discover debris on the road, please call West Sussex Highways on 01243 642105.
To report power lines down, please call 105.
“In an emergency situation, where there is a risk to life, always dial 999.”