The fire on Nevill Road, Hove, broke out in a warehouse chiller, a spokesperson for Waitrose said.
The Brighton and Southwick branches remain open as usual, they added.
The statement reads: “There was a fire in a warehouse chiller at our Hove shop early this morning while the shop was closed, which was quickly contained thanks to the swift action of the fire service and our partners, to whom we’re incredibly grateful.
“The shop will reopen as soon as it’s safe to do so.”
According to East Sussex Fire and Rescue Service, crews were called to the scene at 3.46am.
