The Chile international missed his side's 5-0 drubbing of Aston Villa last weekend and has failed to recover sufficiently from a hamstring problem.
The news will come as a blow to manager Arsene Wenger, as Arsenal look to record back-to-back victories at White Hart Lane for the first time since the 1980s.
"He [Sanchez] is not far away, the Leicester game [on Tuesday] is a possibility," Wenger said. "He is of course very difficult to keep quiet.
"He is training, but it's light training."
"If you review the last two or three months, maybe people understand that he needs time to get his confidence back and to return to his best level," he said.
"We need to analyse the past. It was difficult for him, and it's always hard for a player to come back.
"We are happy that he has stayed as he is a very important player.
"We need to provide him with the tools to improve, as we do with all the players. We push them, make sure they train in a good way and, after, when they have the chance to play, they give their best."
Depending on Southampton's result earlier in the day, Arsenal - who are on a five-match winning run in all competitions - could climb to third in the league, with Manchester United not playing until Sunday, while Tottenham - two points adrift of the visitors - could go fourth.
