Podolski, who has suffered the damaging blow ahead of this Sunday's North London derby against Tottenham Hotspur, picked up the injury during the Gunners' 2-0 win over Fenerbahce in the Champions League on Tuesday.
Wenger told the club's official website: "It is bad news about Lukas Podolski as he will be out for eight to 10 weeks.
"His hamstring is much more damaged than we thought at the start. It is very disappointing and we have paid a very heavy price for that win [over Fenerbahce]. We have to be patient now."
The Frenchman also confirmed that defender Thomas Vermaelen could return to the fold after the international break.