The 34-year-old Manchester United player was carried off the pitch on a stretcher late in the game.
"Michael has got a severely twisted ankle which normally means ligament damage," England manager Roy Hodgson told reporters.
"We won't know that of course until he's had an X-ray or a scan, but it doesn't look good."
Carrick is definitely ruled out of Tuesday's friendly against France at Wembley Stadium, although the game may be postponed following the attacks in Paris on Friday.
(Reporting by Ed Osmond. Editing by Patrick Johnston)
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