The Hoops boss is expected to remain on crutches for the next six weeks while recovering from the surgery.
"My knee got very swollen and it was painful walking. I can't drive for a while," The Sun quotes the 66-year-old as saying.
Redknapp had the procedure on Tuesday and left hospital in a wheelchair the following day.
QPR's first season back in the Championship begins in just over three weeks with a home clash against Sheffield Wednesday.