The service will be offline from 11am to 3pm on Tuesday, meaning customers will be unable to book a ride through the service.
Uber responded to a request to join the protest from the Alternative Mobilité Transport (AMT) association, a group that speaks for around 1,000 private minicab drivers or VTC drivers as they are known in France.
"As many as 10,000 families face financial uncertainty after the job they'd been doing for years was taken away from them," Uber said in a statement to The Local.
"Another 40,000 who wanted to drive have lost this opportunity. Many professional drivers have been protesting in recent days - their fears are understandable - and they have asked us for their support."
Minicab drivers in France say the government unfairly favours ordinary taxis, and minicab drivers have been protesting in Paris since Wednesday last week.
They have been slowing traffic at rush hour and have blocked the entrances to Charles de Gaulle airport, while police keep a close watch and try to redirect traffic.
The protests come after taxi drivers went on a disruptive three-day strike in late January over what they considered to be "unfair competition" from the likes of Uber.
Taxi drivers blocked off roads with burning tyres and staged "go slows" on key roads around the country.
The strike was called off when France's Prime Minister Manuel Valls stepped in and promised better conditions, and "incessant checks" to make sure Uber and other VTC drivers were not breaking the rules.