The ram-raiders targeted Morrisons in Hunslet last night after the store had closed to the public.
Staff were still working inside at around 8.10pm when a white Volvo V60 rammed the shutters at the front of the shop until it broke through them.
A black Kia Sportage was then driven in to the foyer of the store and repeatedly drove at a free-standing cash machine.
Although one suspect jumped over one of the counters, they left empty handed. ã€€
The Kia was left abandoned in the store as the suspects made off in a third vehicle, believed to be a white Mini.ã€€
Detective Inspector Charlotte Hails, of Leeds District CID, said: "This has clearly been a frightening experience for the staff at the store who were understandably shaken.
"There has been extensive damaged caused to the store and it is fortunate that there were no shoppers present at the time. Thankfully no one was injured." ã€€
Police believe at least four suspects were involved, all of whom are described as being white males and wearing dark clothing.
They had their faces covered, wore gloves and spoke with a Yorkshire accent.ã€€
It is believed that the two vehicles used to force entry into the store and ram the cash machine were stolen from the Whinmoor Area of the city on Friday.
The Volvo V60, registration M14 BBN, was being driven on false plates - CV63 PXC.
It has been recovered by police along with the Kia, which has the registration YH17 GZX.
Det Insp Hails said: "I would urge anyone who was in the area around the time of the incident who may have seen anything suspicious or seen the suspects or white mini leaving the area to come forward.
"I would also ask for anyone who has any information about the vehicles or their whereabouts in the days before the incident, or who has seen the white Mini since to speak to police."ã€€
Contact Leeds District CID via 101, quoting 13170126177.
Information can also be passed anonymously to the independent charity Crimestoppers on 0800 555 111.