Asbury School teacher Jennifer Brooke Frazier was placed under arrest at the fields located off Lusk Street near Guntersville Elementary School.
Officers said they had received a call that Frazier had driven her child to practice.
Frazier told WAFF TV48 that she had no alcohol in her system at the time, and claims that a breathalyzer test backs that up – however, that test was reportedly given some eight hours after her arrest.
Frazier made her $500 bond and was released on Tuesday – the public intoxication charge is a misdemeanor.
School officials have thus far refused to comment on the situation.