Calvert-Lewin did the damage in a 2-0 Premier League win at Brighton and Hove Albion on Saturday.
The 24-year-old, who scored his third goal in as many top-fight games this season against the Seagulls, underwent a scan and has been forced to pull out of the squad.
Gareth Southgate has not called up a replacement, so the Euro 2020 runners-up will have a 24-man squad for the three qualifiers.
The Three Lions face Hungary at the Puskas Arena on Thursday before taking on Andorra at Wembley three days later and travel to face Poland at the Stadion Narodowy a week on Wednesday.
England is top of Group I with three wins out of three, leading Hungary by two points.