East Sussex Fire & Rescue Service said they were called to reports of a fire on Nevill Road just before 4am.
Crews have been battling the blaze with jets as police and ambulance services also descended on the scene.
Shocking photos show a huge emergency service presence at the supermarket as smoke filled the sky and roads in the area were closed.
The fire service said they were still working to bring the fire under control at 6am before a later update said they were now working to damp down hot spots and ventilate the property.
No casualties have been reported but the cause of the fire currently remains unknown.
A spokesperson for East Sussex Fire & Rescue Service said: “At 03:46 East Sussex Fire & Rescue Service were called to reports of a fire on Nevill Road, Hove.
“Fire Appliances from Hove, Preston Circus and Eastbourne are in attendance with support from West Sussex Fire & Rescue Service.
“Firefighters are wearing breathing apparatus and fighting the fire with three main jets.
“There are no reports of casualties.”
The Sun has contacted Sussex Police and South East Ambulance Service for comment.
