Palace, who are still on no points and have scored no goals this season, had hoped Zaha would be fit for the clash on October 14 but now expect to be without their key man.
The 24-year-old is suffering from a knee injury and although he has returned to training, his recovery is not yet at a point that Hodgson thinks he can call on him for the clash with Chelsea.
The Eagles are already missing injured striker Christian Benteke and Ruben Loftus-Cheek, who is ineligible against the Blues as part of his loan deal, while Connor Wickham is still weeks away from making a return.
Attacking midfielder Bakary Sako had to play up-front in the 4-0 defeat at Manchester United on the weekend before striker Freddie Ladapo, signed from non-league Margate in March 2016, came on for his debut.
Hodgson has reportedly been offered the chance to sign former Italy international Alberto Gilardino, who is now a free agent, to try to bolster their attacking options.
Speaking after the defeat at Old Trafford, Hodgson said: "We don't have many options — you saw the young boy Freddie Ladapo come on for his first Premier League game after being signed from non-league a couple of years ago, and he's never had a sniff of first-team football.
"That's our choice at the moment or we go to the 4-6-0 system where you don't play with a recognised centre-forward and use a midfielder.
"That's the situation we find ourselves in — I'm not crying or complaining about it."