Shaw left the field early in the first half of the 20-16 reverse and has since had an x-ray to assess the damage.
A Lion in 1997, 2005 and 2009, Shaw's performances for Britain and Ireland's elite last summer reiterated his importance to any potential England resurgence under former Lions team-mate Martin Johnson.
After sending Shaw to see a specialist, the Rugby Football Union has confirmed that he will have an MRI scan later this week.
No comment has yet been made on how long the Wasps star could be out of action for but even minor damage could prevent him from featuring in rounds four and five of the Six Nations.
England face Scotland at Murrayfield on March 13 before travelling to Paris a week later for their final match of the tournament.