Greater Manchester Police believe the thieves spent months digging the tunnel “because of the amount of planning that was involved and complex nature of the tunnel structure.”
The raid took place last Friday on an ATM at Tesco on Liverpool Road, Eccles.
The tunnel went under nearby wasteland and an adjacent building.
DS Mark Toker from Salford Division said: “These people had obviously spent a long time plotting this crime and I doubt they would have been able to keep their plans secret for all that time, without telling others about their elaborate scheme.
“The offenders must have spent long periods of time in the area over the last few months, which people may have noticed.
“You may have seen people acting suspiciously on Friday night, possibly covered in soil.
“I would ask anyone with any information about the robbery to call us as soon as possible.”
Anyone with information is asked to call police on 0161 856 5353 or call Crimestoppers anonymously on 0800 555 111.