The Irishman was not part of the Light Blues squad that spent time in the Highlands last week and missed the matches with Buckie Thistle and Brora Rangers.
In his absence, summer signings Kenny Miller and Kris Boyd both found the target for Ally McCoist's side, and the 31-year-old has now been ruled out of the opening weeks of the campaign.
Daly netted 25 goals in his first season at Ibrox last term and boss McCoist is eager to have him back in action sooner rather than later.
"It looks as though he will be out for six weeks and it's a blow for the team," he told rangers.co.uk
"It's obviously a blow for him, too, but the bottom line is he has to get it sorted as quickly as possible.
"He needs to get back into the swing of things as quickly as possible and he will do.
"I've spoken to him on a couple of occasions and it has settled his mind there is something wrong.
"That might sound a little bit crazy, but if you've got a problem and the doctors and surgeons can't find it, you've got a bigger problem.
"Thankfully we know what it is and it's not a major problem.
"Our doctor has spoken at great length with the surgeon and he's very confident he'll get it cleaned up."