Police are appealing for witnesses after the incident in Bramley on New Year’s Day.
Officers were called at about 2.30am after reports of an explosion at a free-standing cash machine in the car park of the restaurant in Butt Lane.
The gang had pumped gas into the machine and ignited it in an attempt to get to the cash.
While the unit was damaged, the thieves failed to break open the secure section containing the money.
Det Con Phil Joyce, of Leeds CID, said: “This is an unusual method for the offenders to have used and thankfully one which has been shown to be unsuccessful in giving them access to any cash.
“Two suspects were seen near the machine and made off in the direction of Henconner Lane afterwards. I would like to hear from anyone who was in the area at the time and who witnessed the incident.
“I am particularly keen to hear from one potential witness who was described as a white male wearing dark clothing who was walking a German Shepherd dog. It is believed he may have seen the suspects ignite the gas.”
Anyone with any information should call Det Con Joyce at Elland Road via 101 or Crimestoppers, anonymously, on 0800 555 111.