The Englishman sustained the injury in the second half of their first leg Round of 16 Champions League clash, with the winger set to be sidelined for the majority of March.
"We lost Chamberlain on Tuesday, it's quite serious,” Wenger said.
"It keeps him out for a few weeks, he's consulting a specialist. For how long exactly, I don't know.”
However, his club coach allayed fears of the England international missing out on the upcoming European Championships at the end of the season.
"I don't think [there's a danger of missing Euros]," he said.
Chamberlain’s injury came after a strong Javier Mascherano tackle, yet Wenger refused to blame the Argentine midfielder.
"I don't think it was a malicious tackle,” he said. “It was a fully committed tackle.
"Let's hope we get good news and that's it's only two or three weeks, not six or seven."
Arsenal face off against Manchester United in their League clash on Sunday afternoon.
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