The Denmark international opened the scoring late on in the Gunners' victory over Cardiff City on New Year's Day before Theo Walcott added a second.
But Bendtner, a second-half substitute for the recently recovered Lukas Podolski, picked up an injury while scoring the goal.
"Nicklas is a player who has gone through some difficult periods, so I want to give him credit tonight," Wenger told reporters.
"I told him already today, he’s back to his level where I want him to be, and if he continues to give a lot like that he will come back into the team.
"But unfortunately, he got injured today and it looks like it is not a question of days but weeks with a sprained ankle. And I’m very sad for us, but especially for him as well."
Arsenal face an injury crisis up front following the injury to Bendtner, with Olivier Giroud picking up an ankle problem in the win against Newcastle on Sunday, while summer signing Yaya Sanogo has been sidelined for some time.
That leaves Wenger with Podolski and Walcott as his only options, yet the Frenchman refused to be drawn on whether or not Bendtner's injury will force his hand in the transfer market this month.
"I don’t know," he said. "It doesn’t mean we can go from Nicklas’ ankle straight to the transfer market, but it means we have Giroud and Bendtner out."
Bendtner, who has only started two games for Arsenal this season, is out of contract with the club at the end of the season, but Wenger feels the striker has a future at the Emirates.
"We can't stop him from doing it (moving on)," he said. "At the moment he says he wants to stay here. If Nicklas is focused on staying with us and on doing his job, he is a great striker."The 2-0 win against Cardiff puts the Gunners back on top of the Premier League after Manchester City had earlier moved in front of them thanks to a 3-2 win at Swansea.