The 30-year-old reportedly aggravated a long-standing injury to his ankle while on international duty with Nigeria last week.
Some sources had claimed that the striker would need an operation to heal the problem, but Hodgson expects his frontman to feature during Sunday's derby match with Wolverhampton Wanderers.
"There is no question of an operation for Peter," said the boss. "The doctor, Mark Gillett, has a very good relationship with him and whenever Peter has a poor game he looks to his ankle.
"That's what he's been doing ever since I've been at the club - whenever things aren't going his way and he's not in top form, he looks at his ankle.
"I don't know if anything happened in the Nigeria game, but we don't have any information to that effect."
Odemwingie has scored one Premier League goal for the Baggies this season.