The England international has made 35 appearances for the Gunners in all competitions this season, scoring three goals.
But he will miss a number of upcoming matches for Arsenal, including next week's Champions League last-16 second leg at PSG, and also England's games against Lithuania and Italy.
- Arsenal FC (@Arsenal) March 13, 2015
"It is a classic hamstring and that means he will be out for three to four weeks maximum," Wenger said.
"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."
Wenger also announced that Mikel Arteta is back in full training but is still three weeks away while it is "very difficult" to say when Jack Wilshere will be available again after undergoing minor ankle surgery.
"We have to respect the progression of his training and we cannot say when he is back," Wenger said. "I'm hopeful it is a matter of weeks. He had a little inflammation and we had to rest him anyway so we decided to get the screws off.
"At the end of the season, he has England again so we wanted to combine both together. It's taken a bit longer and I don't know why at the moment.".
The Frenchman added: "[Mathieu] Flamini is available and Gabriel will return to training on Sunday."
The Arsenal boss also confirmed that a decision has yet to be made on the future of Arteta, with his contract due to expire at the end of this season.
"I would like him to stay on, he has huge experience and he is very important in the squad," he said.