Welbeck suffered the injury after coming on as a late substitute during Saturday's 1-0 win over World Cup holders Spain at Wembley.
England coach Fabio Capello indicated Welbeck was doubtful on Monday and the 20-year-old headed back to Premier League champions United on Tuesday.
Welbeck made his England debut against against Ghana in March and then featured as a late substitute in a Euro 2012 qualifier with Montenegro in Podgorica last month.
The young forward was praised by Capello for his performance in the final 20 minutes against Spain after replacing Darren Bent.
Welbeck, the latest young player to have his career shaped by long-serving United manager Sir Alex Ferguson, has scored five goals in 12 appearances for the Old Trafford club so far this season.