The former New Orleans Saints defensive end was shot several times during an argument after a traffic accident in the city’s Lower Garden District.
Cardell Hayes, 29, has been charged with second-degree murder, New Orleans police said.
Smith’s wife, Racquel, was also shot in the incident and taken to hospital. The couple have three children.
A Hummer H2 crashed into the back of Smith’s Mercedes-Benz SUV at around 23:30, police said, causing Smith’s vehicle to rear-end another car driven by one of his friends.
Smith and the Hummer’s driver “exchanged words” before the man pulled out a gun and shot Smith a number of times, said police.
“We are thankful for the outpouring of support and prayers,” a Smith family statement said.
“We ask that you continue to respect the family’s privacy as they grieve the loss of a devoted husband, father and friend.”
Smith, originally from Queens, New York, played for Ohio State’s 2002 national championship team and was part of the New Orleans Saints team that won the Super Bowl in 2009.