The 15-year-old student kicked the gate open to free himself after several minutes in the cold, KOAT-TV, Albuquerque, reported.
The teacher's conduct could be criminal, said Santa Fe police detective Sgt. Louis Carlos. The teacher is Abigail Fox. She has worked for the school district for at least 10 years.
"You can see the teacher locking him up," said Carlos, of cell phone video of the incident.
Carlos said the boy was reportedly acting up in shop class on Jan. 7, and the teacher allegedly had students take the boy to the enclosure instead of sending him to detention.
"They keep chemicals in this cage, (like) motor oil, and things not good for you," Carlos said. "(The teacher) could face child abuse and false imprisonment charges. It's disturbing because it's not right."
Carlos said a report will be sent to the district attorney to see if there's enough evidence to charge Fox. The student's name wasn't released because he is a minor.