The 24-year-old suffered ligament damage last Saturday during his side's season-opening defeat to Harlequins at Twickenham Stadium.
"It is a setback for Tom and the club," director of rugby Brian Smith told London Irish's official website. "He has had a great pre-season and was chomping at the bit to be back playing.
"We have an excellent medical and rehab set up at the club and will ensure Tom gets the best possible support to ensure he fully recovers from the injury."
London Irish are back in action this Sunday when they travel to Newcastle Falcons in the Aviva Premiership.