The 25-year-old midfielder twisted awkwardly whilst training and was forced to undergo a minor operation to fix the problem, ruling the player out around for four to seven weeks.
Murphy moved to Elland Road in 2013 from Crewe and has been a regular member of the first-team ever since, making 67 Championship appearances and scoring six goals.
Murphy will now miss all five friendly fixtures over the coming weeks - starting at Harrogate Town on Friday evening - and Uwe Rosler admits the injury is disappointing for both player and manager.
"It's very unfortunate for Luke, I was looking forward to see him in action," he said. "I rate him very highly from my time in League One when he was playing for Crewe. He had a strong end of the season last year and came back to training motivated.
"Everything went his way and went well until he twisted his knee with nobody around him. It's a very unfortunate situation. He needed a minor operation to clear one or two things up and we expect him back within four to seven weeks."