John Henry "Barnie" Barnhill (February 23, 1903 – October 21, 1973) was an American football player and coach and college athletics administrator.

Barnhill was an All-Southern lineman under coach Robert Neyland at the University of Tennessee, including the SoCon champion 1927 team.

In 1946, after Neyland's return to Tennessee, Barnhill was hired by the University of Arkansas as both head football coach and athletic director.

Barnhill died of heart failure on October 21, 1973, at a hospital in Fayetteville, Arkansas.

[4] Barnhill Arena, the former men's basketball and current women's athletic facility at the University of Arkansas, was named for him.