Arsenal will be without the England international for the beginning of the campaign.
The England international has been on the sidelines of late but is set to return to training in the near future.
Welbeck did not play a part in the Gunners’ pre-season Asia Trophy tournament, with the likes of Theo Walcott impressing and stealing a march on the former Manchester United man.
Wenger has confirmed that Welbeck will not be available for the Charity Shield fixture against Chelsea or the first game of the Premier League season against West Ham.
“Welbeck is not in full training yet, he has not fully recovered,” The Daily Mail quote the French coach as saying.
“He is supposed to start to go outside and run again this weekend and from now on, if that is positive in the next three weeks he will be available.
“He will be short for the start of the season in two weeks, but three weeks should be all right.”
Welbeck had an up-and-down first season in North London after leaving boyhood club United last summer.
The versatile forward has made his desire to play as a striker clear, but finds Olivier Giroud as the Gunners’ first choice in the position. Walcott and Alexis Sanchez are also options for Wenger in the number nine role.
Welbeck started 18 Premier League games last season but the majority were from a wide position rather than through the middle.