A farmer and dry goods store owner, he was a resident of Illinois when the Civil War broke out. In August 1861, Ellet was commissioned a captain in the 9th Missouri Volunteer Infantry Regiment, which later became the 59th Illinois Infantry. In March 1862, he fought in the Battle of Pea Ridge. When his elder brother, Col. Charles Ellet, Jr., undertook the conversion of several river steamers to rams in the spring of 1862, Alfred Ellet became lieutenant colonel of Charles Ellet's U.S. Ram Fleet.
Following Charles Ellet's death in June 1862, Alfred took over the unit and was appointed brigadier general of the newly formed Mississippi Marine Brigade the following November. He commanded the Mississippi Marine Brigade during operations on the Western Rivers until 1864, when the unit was disestablished. He resigned his commission late in that year to return to civilian life.
Following the Civil War, Ellet was a businessman and civic leader in El Dorado, Kansas, where he died. He is buried there in Belle Vista Cemetery.