School officials sent home a letter to parents at Millennium High School telling them what happened.
The teacher has been placed on leave and was booked Thursday into the 4th Avenue Jail.
Goodyear Police arrested 31-year-old Jared Blackstone on one count of luring a minor for sexual exploitation.
A search warrant was executed at his home Thursday, part of an active investigation into the teacher's conduct.
The school district was contacted by a parent that saw a conversation on a blog alluding to the relationship between the teacher and student. The district notified police of the allegation and an investigation was started.
The district issued a statement as follows:"Recently, the administration contacted Goodyear Police regarding an allegation of an improper relationship involving one of our staff members and a student. A police investigation is in progress. School and District personnel are cooperating fully with the police.
The safety of the students and staff is the District's highest priority. The school and District will continue to cooperate with police and will take every step necessary and appropriate to maintain the high standards we hold for our students and our staff."