The Tongan, who joined Tigers from London Welsh this season, was injured in Sunday's 24-16 victory over Wasps.
Director of rugby Richard Cockerill told BBC Radio Leicester: "He broke his arm tackling so is probably six to eight weeks from getting back, which is disappointing after a good start."
But Tommy Bell, Sebastian de Chaves, Ed Slater and Graham Kitchener are fit.
All four could all be available for Saturday's Premiership match at Exeter Chiefs.
Locks Slater and Kitchener would be making their first appearances of the season but Cockerill said he will be cautious about their return to action.
"They are all likely to be available so we will see how much game time they get," he added. "We will take a hungry squad to Exeter."
Leicester Tigers number eight Opeti Fonua could be out of action until late December with a broken arm.