The Arsenal forward is emerging as a doubt for Arsenal's next four fixtures and England's forthcoming World Cup qualifiers against Slovenia and Lithuania after limping off during the second half of Sunday's draw at Chelsea.
And after Welbeck had a scan on Monday, Wenger confirmed that he would not be able to return this month.
He underwent a scan yesterday and is due to have another today to reveal the full extent of the injury.
The 4 fixtures he will not feature in if he is out up till the global break would be Carabao (EFL) Cup game against Doncaster, Premier League clashes against West Brom and Brighton, and the Europa League fixture at BATE Borisov.
Early estimates place the England global at being sidelined for four weeks, but a more certain length of recovery time will be known soon enough.
Arsenal's Welbeck out at least three weeks
Arsenal are unlikely to take any chances with Welbeck's recovery given his history of injury problems.
The English worldwide is also likely to miss World Cup qualifiers against Slovenia and Lithuania.
Welbeck's Arsenal career has been blighted by various injuries since he made the surprise £16m from boyhood club Manchester United in the summer of 2014.
One name which will be missing, however, is Danny Welbeck, after the England striker suffered yet another injury setback.