He was caught attacking the Alverley Express BBQ House, Springwell Lane, Balby, at 11.45pm on Thursday, January 28.
The vandal is then said to have attacked the owner’s car which was parked nearby - smashing the windows and slashing the tyres.
South Yorkshire Police said the man was wearing a two-tone blue hooded jacket and had his face covered.
He ran away towards Galsworthy Close and it is thought he may have got into a vehicle.
A South Yorkshire Police spokesman said: “Officers are keen to hear from anyone who witnessed the incident or who saw anyone acting suspiciously in the area. Can you help?”
Anyone with information should call South Yorkshire Police on 101.