Szczesny has been hampered by an ankle problem all summer, and has only been fit enough to start two games for Arsenal in the early weeks of the season.
Wenger revealed that Vito Mannone will continue to deputise for the Polish keeper for at least the next fortnight.
The Gunners boss said: "We have still Szczesny injured, plus Lukasz Fabianski.
"Szczesny is still two to three weeks away at the moment."
Mannone has kept two clean sheets in Szczesny's absence and helped Arsenal secure a 1-1 draw against reigning champions Manchester City in their last league match.