Footage shows the hooded man marching up to the restaurant counter before opening the gate and entering the kitchen area while clutching a blade.
He is seen to grab the box, containing dozens of promotional Monopoly cards and vouchers, from a tray before waving the knife at a cashier who attempts to intervene.
Police have released the footage in an attempt to trace the suspect following the robbery on Coldharbour Lane on 23 March at 2pm.
He is described as a black man, dressed in a dark and grey two tone hooded top, with white gloves, black trousers and black shoes.
Detective constable Emma Brookes, of Hillingdon CID, said: “We are appealing for anyone who may know who was involved in this robbery.
"Although he had his face covered, it is possible that someone may recognise his clothing or may have heard someone talking about this robbery.”