John A. Quickel was born on February 12, 1831, in Pennsylvania to George and Susan Quickel. The family lived in Conewago, Pennsylvania, and his father died around 1845. By 1850, he was living with relatives in York, Pennsylvania, and working as a carpenter. He married Mary Jane Axe around 1853, and their son Henry was born around 1857. They settled in Mechanicsburg, Pennsylvania, and by 1860, he owned $600 of real estate.
Quickel enlisted in the Union army on September 13, 1861, and he mustered in as a private in Company E of the 87th Pennsylvania Infantry later that day. He took part in the Second Battle of Winchester, the Bristoe campaign, and the Battle of Mine Run. He was severely wounded in the arm at Mine Run, and surgeons amputated the limb soon afterward. He was discharged on February 15, 1864. He applied for a federal pension a week later and eventually secured one.
Quickel returned to Mechanicsburg after the war and earned a living as a watchman. By 1870, he owned $1,500 of real estate and $300 of personal property. He and Mary Jane may have separated sometime in the 1870s, and he apparently settled in Conewago, Pennsylvania. He died on June 9, 1888.