Welbeck sustained the hamstring injury in the 8-2 win over Arsenal at Old Trafford earlier on Sunday.
The young forward will miss England’s Under-21 games against Azerbaijan and Israel in September.
“It is a loss for us and for England,” boss Sir Alex Ferguson told BBC Sport.
“Danny complained of a tight hamstring before he actually pulled it and we couldn’t get [Javier] Hernandez on quick enough,” continued Ferguson.
“It is a shame for Danny but it [his absence] will be around four to five weeks.”
