The Spaniard is expected to be on the sidelines for the next three months after undergoing surgery to rectify an Achilles problem.
Cazorla has not featured for the Gunners since picking up the injury during the team's 6-0 victory over Ludogorets Razgrad in the Champions League on October 19.
After the inflammation failed to ease, the club decided that surgery was the only answer, but it means that Arsenal will be without Cazorla for the hectic festive period.
"For me it is very bad news," Wenger told reporters in Friday's press conference. "There is not a date [for his return]. I try to put everything into place to avoid surgery. It creates anxiety, rehabilitation and if you can avoid it you do.
"In this case we have come to the conclusion [of surgery], and now they tell me he will be out for two months at least, but two months can sometimes be three.
"Santi is desperate to play football, he is only happy when he is playing football and just wants to cure it. He has inflammation in the back of his foot, which no-one knows where it is coming from. The anti-inflammatory injections have not got rid of it. The specialist we discussed it with said he had to open it up."