The England international sustained the injury in the Gunners’ 2-1 win at Manchester United on Monday, which booked their place in the FA Cup semi-finals.
Oxlade-Chamberlain had only just returned to the fold after a groin problem, which had kept him out of action for five weeks this year.
The 21-year-old has suffered a number of injuries during his career at the Emirates, most notably his knee which ruled him out for the first half of the 2013/14 season.
Commenting on the injury, Wenger said on the club’s Twitter account: “It is a classic hamstring and that means he will be out for three to four weeks maximum.
“In the last few months he has been a bit in and out, but he showed again on Monday what an important player he can be for Arsenal and England and it is a shame that in the final sprint he is not there.
“How much will it affect him [mentally] I don’t know. He loves to play and he is keen to play for England as well and it is a big blow for him, but he knows that this kind of injury he can recover quickly and he can come back, but it is not an ideal moment.”