Emergency services were called to the site at 100 Wardour Street, Soho, after a blaze began inside the kitchen of one of the restaurants.
There were no reported casualties although 20 people were evacuated from the building.
The restaurants ceased trading over the weekend and the websites of both confirm they will ‘be closed for business until further notice’.
D&D London said in a statement: "Due to a fire at 100 Wardour Street, D&D London’s Soho venues, pan-Indian restaurant and cocktail bar Carom and iconic late night venue Floridita, are currently closed.
"There were no injuries and the management are working to have the venues back up and running as soon as possible."
A spokesperson from the restaurant group told BigHospitality that it was hoped the sites would re-open in just over a week, although there was currently no confirmed date.