Carrick, 34, suffered the injury late on in Alicante on Friday evening and left the pitch on a stretcher.
England boss Hodgson said: "Michael has got a severely twisted ankle which normally means ligament damage.
"We won't know that of course until he's had an X-ray or a scan, but it doesn't look good."
Carrick will definitely miss Tuesday's scheduled friendly with France at Wembley.
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Manchester United midfielder Michael Carrick may have suffered ankle ligament damage during England's 2-0 defeat in Spain, says Roy Hodgson.