The right-back has enjoyed a fine start to the season with the Reds and was rewarded with a first senior international call-up by manager Gareth Southgate, ahead of the European Championship qualifiers against Bulgaria and Kosovo.
Despite training with his colleagues at St George's Park, he has had to return to United for treatment.
As Liverpool's Trent Alexander-Arnold and Atletico Madrid defender Kieran Trippier are already in the England squad, no replacements are planned.
The withdrawal will be a disappointment for Wan-Bissaka, who has previously impressed at Under-21 level for his country.
Ole Gunnar Solskjaer will be hoping the 21-year-old is available for United's next assignment, the Premier League fixture with Leicester City at Old Trafford on 14 September.