The 25-year-old is facing up to seven weeks on the sidelines due to an injury sustained in training at Thorp Arch.
Murphy twisted a knee towards the end of a pre-season session last week and was sent for an operation after seeing a specialist.
The news is a blow to new head coach Uwe Rosler and will intensify the club’s search for another central midfielder.
Murphy - a £1m signing from Crewe in 2013 - rediscovered his form in the second half of last term having previously fallen out of favour at Elland Road.
Rosler, whose side start the 2015-16 Championship term at home to Burnley on August 8, said: “He twisted his knee without anyone around him.
“It was a very unlucky situation and the last minute of the training session. He’s already gone for a small procedure on his knee.
“I don’t think we’ll have him back ready to play in the first game against Burnley. We’ll be thinking between four and seven weeks, something in between that.
“It’s a minor thing but it had to be done. I’m sad for Luke because he really tried to impress and he finished last season strong.”
Murphy is the only confirmed absentee ahead of Leeds’ first pre-season game at Harrogate Town tomorrow night.
On trial right-back Adam Drury is continuing to train with Leeds and could feature at Harrogate but goalkeeper Jak Alnwick has moved on after a brief trial at Thorp Arch.