It happened on the famous Promenade des Anglais after a firework display. The driver was shot dead and guns and grenades were found inside the lorry.
President Francois Hollande said the attack was of a "terrorist nature".
He extended a state of emergency across France by three months.
France had been on high alert following last November's attacks in Paris in which 130 people died and hundreds were wounded.
The state of emergency had been due to end on 26 July.