Officials at the school in Rio Rancho, about 15 miles north of Albuquerque, announced Friday that the teacher recently was disciplined for his comments to the student, but they declined to say how, KOB-TV reported.
The move came after students at Cleveland High School were told they could come to class dressed as Santa, an elf or a reindeer.
Michael Rougier said his ninth-grade son, Christopher, arrived wearing a Santa hat and beard, and the teacher asked the boy: "Don't you know Santa Clause is white? Why are you wearing that?"
The teacher's name was not released, and attempts by The Associated Press to reach school officials Saturday were unsuccessful.
Michael Rougier said the teacher's comments enraged him.
"There's no room for that in the classroom," he said. "Whether this teacher felt Christopher may have been wearing this out of context, there's no room for it. There's just no room for it."
The incident happened the same week that Fox News Channel's Megyn Kelly said on the air that both Santa Claus and Jesus were white. Her comments drew national attention and prompted a slew of heated comments on blogs and social media sites.
A spokesman for Rio Rancho Public Schools said the Cleveland High School teacher knows he made a "dumb" mistake and has since apologized to the Rougier family.
Michael Rougier said he still has concerns. "If he has that attitude, how is it affecting students, studies, grading habits, trending toward Caucasian kids?" Rougier said of the teacher.
The teacher still works at Cleveland, but Christopher has been removed from his class, KOB-TV reported.
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