Brashear died at the Naval Medical Center Portsmouth of respiratory and heart failure, the medical center said.
Brashear retired from the Navy in 1979 after more than 30 years of service. He was the first Navy diver to be restored to full active duty as an amputee, the result of a leg injury he sustained during a salvage operation.
"The African-American community lost a great leader today in Carl Brashear," Gooding said of the man he played alongside Robert DeNiro, who was Brashear's roughneck training officer in "Men of Honor." "His impact to us as a people and all races will be felt for many decades to come."
In 1966 Brashear was assigned to recover a hydrogen bomb that dropped into waters off of Spain when two U.S. Air Force planes collided.
During the mission Brashear was struck below his left knee by a pipe that the crew was using to hoist the bomb out of the water. Brashear was airlifted to a naval hospital where the bottom of his left leg was amputated to avoid gangrene. It later was replaced with a prosthetic leg.
The Navy was ready to retire Brashear from active duty, but he soon began a grueling training program that included diving, running and calisthenics.
"Sometimes I would come back from a run, and my artificial leg would have a puddle of blood from my stump. I wouldn't go to sick bay because they would have taken me out of the program," Brashear said in 2002 when he was inducted into the Gallery of Great Black Kentuckians. "Instead, I'd go hide somewhere and soak my leg in a bucket of hot water with salt in it -- that's an old remedy I learned growing up."
Brashear faced an uphill battle when he joined the Navy in 1948 at the age of 17, not long after the U.S. military desegregated.
"I went to the Army office, and they weren't too friendly," Brashear said in 2002. "But the Navy recruiter was a lot nicer. Looking back, I was placed in my calling."
Brashear, the son of poor sharecroppers in Sonora, Kentucky, quickly decided after boot camp that he wanted to become a deep-sea diver.
"Growing up on a farm in Kentucky, I always dreamed of doing something challenging," he said. "When I saw the divers for the first time, I knew it was just what I wanted."
In 1954 he was accepted and graduated from the diving program, despite daily battles with discrimination, including having hate notes left on his bunk.
He went on to train for advanced diving programs before his 1966 incident.
"He kept to himself personally, but his military life was an open book," said Junetta Brashear, his first wife, who lives in Portsmouth, Virginia, near Brashear's home in Virginia Beach.
She said Brashear's health started to deteriorate about three years ago, but that he had experienced problems ever since the amputation.
Brashear married childhood friend Junetta Wilcox in 1952 and had four children -- Shazanta, DaWayne, Phillip and Patrick -- before their divorce in 1978. He later married Hattie R. Elam and Jeanette A. Brundage.
Funeral arrangements are pending.