He is expected to miss Wednesday's Carabao Cup match against Doncaster, Premier League games with West Brom and Brighton, and a Europa League fixture against Bate Borisov.
Having undergone a preliminary scan on Monday, the England worldwide is set for a second scan today to give a definitive assessment of his groin injury according to reports.
Arsenal's forward, Danny Welbeck will be out at least until after next month's worldwide break with a groin injury sustained in the match against Chelsea at Stamford Bridge on Sunday.
With two weeks off for the October worldwide break, the time table for return, at the earliest, is almost a month from now.
But he is nearly certainly out of England's final two World Cup qualifiers against Slovenia and Lithuania early next month.
Wenger, meanwhile, also gave updates on crocked midfielders Mesut Ozil and Francis Coquelin. Goalkeeper David Ospina, club captain Per Mertesacker, Mohamed Elneny, Ainsley Maitland-Niles, Theo Walcott, Alexis Sanchez and Olivier Giroud all started against Cologne in the Europa League win last Thursday before missing the Chelsea game. "He has a little inflammation of his knee".
The England global suffered the injury in the last quarter of the Gunners' goalless draw with Chelsea on Sunday.
Defender Calum Chambers will be included against the League One team, as the Gunners start their bid for a first League Cup since 1993.
The younger players will be hoping to be given a chance in the League Cup, a tournament manager Arsene Wenger has previously used to blood academy talent into first-team football.
Six injured in acid attack at London station
The 28-year-old added: "There were cuts around his eyes and he was trying to chuck water into them". Outside, people gathered at police cordons while victims were being treated behind a blue screen.