Tuilagi joins fellow centres Anthony Allen and Matthew Tait on the sidelines. Allen is expected to be out for three months after suffering a thumb injury in a DIY accident and Tait is not expected back until December after aggravating a groin injury.
Allen has already undergone surgery on the injury but is expected to be ruled out of the former Champions' entire Heineken Cup Pool campaign, while Tuilagi looks set to miss out on his side's opening four games in Europe.
"Our luck is not getting any better, is it?" said director of rugby Richard Cockerill.
"Manu's was just one of those things in a collision. It's a straightforward break and he will be out for six weeks.
"Ant (Allen) was doing some DIY at home and cut his thumb.
"He has had surgery and it will take three months to heal."