He was diagnosed with colon cancer more than four years ago, according to his website.
The famous song, "with its crackling bluesy guitar and insistent cowbell, was one of the most exciting early rockabilly singles," music historian Richie Unterberger wrote of "Susie-Q" on the Allmusic Internet database.
The single reached the top 30 in the U.S. in 1957 and was later covered by many artists, including the Rolling Stones and Creedence Clearwater Revival, which had a top 20 hit with the song in 1968.
The raw, bluesy swamp-rock sound of the original "Susie-Q" grew out of a childhood steeped in rural country and blues music.
He was born Delmar Allen Hawkins on Aug. 22, 1936, on a plantation in Gold Mine, La., to a country musician and his wife, who was a teacher and day worker.
Growing up, Hawkins was exposed to a wide range of live music while riding with his sheriff grandfather on Saturday night patrols.
At 16, Hawkins lied about his age to join the Navy, he later said, and served in the Korean War.
He formed a small musical combo in 1955 that included a teenage James Burton, whose guitar lick would be crucial to "Susie-Q."
When "See You Later, Alligator" became a hit for Bill Haley, Hawkins responded with “See You Soon, Baboon.” Some of his better-known songs included “My Babe” and “La-Do-Dada.”
In the 1960s, Hawkins turned to producing, creating top 10 hits for Bruce Channel ("Hey! Baby") and the Five Americans ("Western Union").
He went through a lengthy drug rehabilitation program in the early 1980s, and he opened a crisis-intervention program in the South for teens.
His first album of new material in 30 years, "Wildcat Tamer," was released in 1999. The affecting "Back Down to Louisiana" followed in 2007.
When asked what he would tell musicians who aspired to follow him, Hawkins once said: "Study the masters, man. . . . Grab the roots and see how it evolved and know what's real."
Hawkins is survived by sons Jeffrey and Jay Paul; his brother and sister; and three grandchildren.