Hodgson's outstanding form this season has helped guide Saracens into second place in the Aviva Premiership and underpinned an unbeaten start to their Heineken Cup campaign.
But he was hurt during the closing stages of last Sunday's Premiership victory over Wasps and has now undergone surgery.
It is thought that Hodgson could struggle to play again before Christmas, although Saracens have not put an exact timescale on his recovery.
The 31-year-old Yorkshireman joined Saracens from Sale Sharks and won 36 England caps. He retired from Test rugby earlier this year.
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