Born in Waxahachie, Texas, Kirksey moved to the San Francisco Bay Area when he was about thirteen years old and graduated from Palo Alto High School in 1913.
At the 1920 Olympic Games in Antwerp, Kirksey finished second in the 100-meter sprint behind Charlie Paddock. Six days later he anchored the United States 4x100-meter relay team that won the gold medal in a world record time of 42.2 seconds. Two weeks later Kirksey won his second gold medal, helping the American rugby team defeat France 8-0.
As a Stanford University student, Kirksey won the IC4A championships in 100 yd (91 m) in 1921 and repeated the Paddock's world record in 100 yd (91 m) of 9.6.
Kirksey earned a bachelor's degree in philosophy from Stanford and then a degree from St. Louis Medical College. He worked as a staff psychiatrist for the state Department of Corrections, assigned to San Quentin and Folsom prisons.
Morris Kirksey died in San Mateo, California, at the age of 86.