Zaha suffered a shoulder injury during last weekends 2-2 draw with Arsenal and did not feature for Palace as they were knocked out of the Carabao Cup on Wednesday.
But Hodgson expects Zaha to return for the Eagles against Chelsea, and also said Palace would support the 25-year-old after he revealed he has received racist abuse on social medial following the Arsenal fixture.
He was fine the last time I saw him, said Hodgson. He took a bang on the shoulder at the weekend which will be fine by the Chelsea game.
It would have been difficult to play him [against Middlesbrough] with that knock anyway, but I spoke to him yesterday and he said he was fine.
The club will do everything they can to support him [over the abuse].
I do not think there are many people out there, perhaps the odd social media troll who knows no better, who believes that racially abusing people or threatening people is the right way to go.
It is fairly obviously that, at my stage of life, I do not have any sympathy for people who use these platforms to abuse other people.
The club will do everything they can to help him get through the situation.
In Zahas absence, Crystal Palace suffered a 1-0 defeat to Championship side Middlesbrough in the fourth round of the Carabao Cup on Wednesday.
Boro will now face Burton Albion in the quarter-finals of the competition.
Of course it is a missed opportunity, Hodgson added. If that [Middlesbrough playing Burton in the next round] is the case, then even more so.
But we have had a fairly stable XI this season and there were a lot of players there tonight who needed a game.