The England international sustained the problem five minutes into the second half at Old Trafford and was subsequently replaced by Aaron Ramsey - with reports suggesting he could be out for up to four weeks.
However, Wenger insisted there was no prognosis yet, while offering mixed news on the availability of Jack Wilshere (ankle), Mathieu Flamini (hamstring) and Gabriel (hamstring) ahead of Saturday's Premier League clash with West Ham.
"Chamberlain has a hamstring strain," Wenger told the club's official website.
"The only thing we don't know is how bad it is because usually the scans are only done 48 hours after the accident. That will be done today [Wednesday].
"Jack is progressing well, he is not back in training yet. Mathieu is training, he could be available for the squad on Saturday.
"Gabriel may be [available] next week, he should come back into training on Sunday or Monday."
