Chiles, a fervent Baggies fan, was hosting at the club's annual awards evening on Sunday when he made a foul-mouthed aside about the forward.
Odemwingie, who became a target of abuse when he attempted to force through a move to QPR in January, was not present at the ceremony having been given permission by Clarke to stay away.
But Clarke was clearly unimpressed by Chiles' conduct.
"I thought it was out of order," he said.
"It was just a ridiculous comment to make. It was a stupid comment and it was out of place. It was a West Bromwich Albion awards night and there was no place for that kind of comment.
"I protect my players fiercely and I didn't like it.
"It was a throw away line from someone who should know better."
Odemwingie has not played for the club since a substitute's appearance on March 30, but Clarke insists he could still play a part before the end of the campaign - starting with Saturday's match against Wigan.
"He's not frozen out - I don't do that to my players," said Clarke.
"My relationship with players is important to me and my relationship with Peter, and all my players, is good.
"He's an attacking option for the weekend for sure. He's in my thoughts."