The two were driving to attend a football game at Pascagoula High School, where both of them played.
The son was redshirting this season as a true freshman for the Bulldogs (No. 20 CFP, No. 24 AP), who were off this weekend after beating Missouri on Thursday night. Joseph Sr., 44, ranks 10th all time in MSU history with 14 sacks.
"We are deeply saddened and heartbroken by the tragic loss of Keith Jr. and his father," Mississippi State coach Dan Mullen said in a statement. "Keith had such a promising future as a Bulldog following in the legacy started by Keith Sr., who played for our program 25 years ago.
"Keith was a great student, a hard worker and a great teammate to all of us. With heavy hearts, our thoughts and prayers go out to the Joseph family, our entire Mississippi State community and all of the lives these Bulldogs touched."
Funeral arrangements are pending. Details of the accident weren't immediately available.
"Words can't express the sorrow we feel by having lost not one, but two members of the Bulldog family, father and son," Mississippi State athletic director Scott Stricklin said. "I was a classmate of Keith Sr., and took pride in having Keith Jr. follow in his dad's footsteps at MSU. They will both be missed greatly. It's such a tragic reminder that life is a precious and every day is a gift from God."
The school also paid tribute to the Josephs via Twitter.