The German limped off in Arsenal's 2-0 win over Fenerbahce shortly after half-time with a hamstring injury, although the Gunners had hoped the injury was not as bad as it first appeared.
But Wenger and his staff have now learnt that the 28-year-old will be sidelined for at least two months.
"It is bad news about Lukas Podolski as he will be out for eight to 10 weeks," Wenger told the club's official website.
"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."Wenger did reveal, however, that midfielders Jack Wilshere and Aaron Ramsey should be fit to feature in Sunday's north London derby against Tottenham despite the knocks they picked up against Fenerbahce.
"The news is quite positive. They just had bumps and bruises. They will be involved," Wenger added.
Meanwhile, the Frenchman also gave an update on the progress of Arsenal's long-term absentees.
He continued: "[Mikel] Arteta is doing okay but there are few weeks to go with him. Thomas Vermaelen could be back after the international break."