Bianchi is facing an absence of up to six weeks and looks unlikely to be available until the middle of September due to a cartilage problem suffered 10 days ago.
The Italian was hurt during United’s pre-season friendly against Eintracht Frankfurt and missed their 2-1 defeat to Hoffenheim in Norway last weekend.
Head coach Uwe Rosler hoped Bianchi would resume training this week but fresh analysis of the 26-year-old’s condition forced Leeds to send him for an operation.
The injury is unrelated to the cruciate ligament damage which saw him undergo surgery towards the end of last season but Rosler was disappointed to lose a player who featured regularly in the early stages of the summer.
Fellow midfielder Luke Murphy is already recovering from a similar operation and is due to return towards the end of next month.
Rosler said: “It’s a pity because I felt Tommaso was one of the players who really came on.
“He did every training session but then against Frankfurt he got an impact injury. He damaged cartilage, a similar injury to Luke Murphy. We think he’ll be out for four to six weeks.”