Police shot and killed the driver, who drove the heavy, long-distance truck at speed for well over 100 metres along the famed Promenade des Anglais seafront, hitting the mass of spectators late in the evening, regional official Sebastien Humbert told France Info radio.
The man had opened fire on the crowd, local government chief Christian Estrosi told BFM TV, and weapons and grenades were found inside the truck after he was killed.
"It's a scene of horror," local member of parliament Eric Ciotti told France Info, saying the truck had sped along the pavement fronting the Mediterranean, before being stopped by police after "mowing down several hundred people".
Local broadcasters quoted officials as saying the preliminary death toll was 73. Other officials put the number of wounded as high as in the hundreds.
Humbert described it as a clear criminal attack, although the driver was not yet identified. Residents of the Mediterranean city close to the Italian border were advised to stay indoors. There was no sign of any other attack.
Nice-Matin paper published a photograph of a damaged, long-distance delivery truck, which it said was riddled with bullets and images of emergency services treating the injured.
The city, with a population of some 350,000 and a history as a flamboyant but also gritty metropolis in the sun, has seen some of its Muslim residents travel to Syria to fight, a path taken by previous Islamic State attackers in Europe.
