The Denmark striker suffered an ankle injury when scoring the opening goal in the 2-0 Premier League victory over Cardiff City on New Year’s Day.
Bendtner was sent for a scan and Wenger revealed on Saturday after the 2-0 victory over Tottenham that the 25-year-old will be sidelined for around four weeks, leaving the Premier League leaders short of options in attack.
Theo Walcott was employed in his preferred position as a striker against Tottenham, but the England international was carried off with a knee injury late on.
The former Southampton man did not appear to be in pain as he gestured to Tottenham fans to remind them of the score when he was carried off.
Wenger will wait to discover the extent of Walcott's injury and revealed the away supporters had pelted his player with coins.
He said: "Theo has a knee problem, we don't know if it is a stretched ligament or just a kick.
"I've seen the pictures (of Walcott's gesture) afterwards. It does not even look aggressive, it's smiley. The doctors said to me the coins were raining over his head and that is why."
Goals from Santi Cazorla and Tomas Rosicky ensured Arsenal progressed to the fourth round at the expense of their arch-rivals.
And Frenchman was impressed with the manner in which they got the job done.
He said: "The game was played at a good pace and we controlled quite well both sides of it, the defensive and offensive."
Wenger also confirmed that Olivier Giroud will return for the clash at Aston Villa a week on Monday after missing two games with an ankle injury.
Thomas Vermaelen was taken off at half-time, but Wenger stated the Belgium defender had been on the end of a kick and his injury was not serious.
