The 30-year-old will also miss the friendly in France on 13 June.
A Football Association statement said Vardy suffered the problem in training on Tuesday.
Manager Gareth Southgate will not call up a replacement, with Jermain Defoe, Harry Kane and Marcus Rashford the strikers in the squad.
England are four points clear of Slovakia at the top of Group F after five of the 10 games.
Striker Jamie Vardy has withdrawn from the England squad for Saturday's World Cup qualifier against Scotland at Hampden with a "minor injury".