Powell stopped Houston Texans' running back Ryan Moats for running a red light near a hospital in Plano, Texas. Moats' mother-in-law, Jonetta Collinsworth, 45, a breast cancer patient, died before either he or his wife reached her room.
Moats was driving his wife, Tamisha, to visit her dying mother at the Baylor Regional Medical Center.
During a 13-minute confrontation, Powell wrote a traffic ticket and drew his weapon.
After extensive national media coverage, Powell was placed on administrative leave after the incident.
"With a heavy heart and great sadness, I resigned from the Dallas Police Department this morning," Officer Robert Powell said in a written statement to the Dallas Morning News. "I (hope it) will allow the Dallas Police Department, my fellow officers, and the citizens of Dallas to better reflect on this experience, learn from the mistakes made."