Sancho missed England's 4-0 win in Hungary on Thursday due to the problem he suffered in training.
The 21-year-old will play no part against Andorra at Wembley on Sunday or in Wednesday's clash with Poland in Warsaw.
"Following further assessment, the 21-year-old has returned to his club and is expected to recover in time for Manchester United's fixture with Newcastle United on Saturday September 11th," an English Football Association statement said on Saturday.
Sancho has featured in all of United's Premier League matches since joining Borussia Dortmund in the close-season.
He made his first start for Ole Gunnar Solskjaer's team in the 1-0 win at Wolves before the international break.
Sancho, who has three goals in 22 appearances for England, saw his penalty saved in the Three Lions' shootout defeat against Italy in the Euro 2020 final in July.
Standout matches today