Rashad Wayne was pronounced dead at the scene, said James Gallagher, a spokesman for the Kenner Police Department.
Police responded to a call at 10:15 a.m. Sunday about a wreck on westbound Interstate 10. Officers found a Capital City Produce Company truck stopped in the highway's right lane and found the 32-year-old Wayne in the cab with a severe head injury.
A preliminary investigation determined that the truck was traveling in the left lane on the upramp of the interstate bridge, but it crossed three lanes as it started fishtailing and then hit the right retaining wall, Gallagher said.
"It slid along the top of the wall on its side a short distance before landing back on its wheels across the lanes leading to Interstate 310," he said.
Rashad Wayne is from Baker, north of Baton Rouge. An autopsy will be performed.
His brother, Reggie Wayne, a New Orleans native, is in his sixth year with the NFL. Wayne played in the Colts' 21-14 home victory over the Jacksonville Jaguars on Sunday, then boarded a plane for Louisiana, Indianapolis television station WISH reported.