The Three Lions will face their neighbours to the north in a World Cup qualifier at Hampden Park in Glasgow on Saturday before facing the French in a friendly on Tuesday.
Vardy will not be replaced, leaving the English with three options up front: Premier League top scorer Harry Kane of Tottenham, veteran Sunderland striker Jermain Defoe, and Manchester United teenager Marcus Rashford.
"Jamie Vardy has left the England squad as a precaution after picking up a minor injury in training at St. George's Park yesterday.
"The Leicester City striker won't play a part in either Saturday's World Cup qualifier in Scotland or Tuesday's trip to France.
"No further players are due to be added to the squad at this moment in time."
England currently lead the standings in Group D of qualification for Russia 2018, four points clear of second place Slovakia, while the Scots are in need of a win to keep up the pace.
