The 34-year-old, who picked up the injury during the warm-up for Saturday's 6-0 win over San Marino that booked a place at the finals, has returned to Manchester United for treatment.
"It's a calf injury. We don't believe it's that serious. It's quite strange because it came out of nowhere almost," England manager Roy Hodgson told a news conference on Monday.
"It was at the start of the warm-up in San Marino that he felt something very small, very slight so just out of precaution we didn't push that side of it -- the same with the work after the training.
"He had a preliminary type of scan, a very simple one if you like, here with our doctors and they decided there's something there," Hodgson added.
"It's up to Manchester United now of course to... look at it much more closely. We don't think it's a long-term injury but, of course, more than enough to keep him out of the game which both he and I are very disappointed about."
Carrick, who has 33 caps for England, has played in all four of United's Premier League games so far this season.
His injury could mean Swansea City midfielder Jonjo Shelvey getting another start after his impressive performance against San Marino although Hodgson said there were other options.
"... we have Fabian Delph, who played well in the game, we have Ryan Mason, we have James Milner, who is capable of playing in other positions. We have options in that area without radically changing our system of play," noted Hodgson.
(Reporting by Ken Ferris; Additional reporting by Simon Jennings in Bengaluru; Editing by Sudipto Ganguly and Ken Ferris)
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