Traffic in and out of the airport's two terminals was disrupted and a woman taxi driver was knocked down, with the driver's union threatening to stage another blockade on Friday.
The injured driver was taken to hospital but told AFP no bones had been broken after she was hit by a rival working for a ride-hailing service.
But she is filing a complaint with police after being left “covered in bruises”.
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A police source told AFP tensions between the rival drivers traditionally escalate ahead of the world's biggest film festival, which runs from May 14 to 26.
“It's always the same during the Cannes festival, the taxis line up in front of the private hire cars and it becomes a game of cat-and-mouse, it's not a brawl but it can get really crowded and things can get out of hand,” he said.
Fabrice Cavallera, who heads the Nice taxi drivers' union, said they suspended the protest mid-afternoon but would resume the strike on Friday if the authorities did not impose restrictions on their ride-sharing rivals.
As part of an anti-fraud drive, taxi drivers have been faced with a series of impromptu checks, which they say private hire drivers have so far escaped.
Police were called in to break up the protest. Some drivers said travellers were forced to walk part of the way to the airport in order to avoid missing
May is a busy month for Nice's Cote d'Azur airport which sees a 15 percent increase in numbers due to the Cannes film festival and the Monaco Grand Prix.