The attack took place near the city's main opera house in an area full of bars, restaurants and theatres which were brimming on a weekend night.
The man attacked five people with a knife, one of whom died, police said. Two were in serious condition and all the victims are in hospital.
Interior Minister Gerard Collomb hailed in a tweet the "sang-froid and reaction of the police who neutralised the attacker."
A large area was cordoned-off where police, fire and rescue vehicles converged.
Shocked tourists and residents looked on from behind the security perimeter.
"I was on the cafe terrace, I heard three, four shots, it happened very fast," said 47-year-old Gloria.
"Then the bartenders told us to come inside very quickly. Then I went out to see what was going on, and then I saw a man on the ground," she added.
Police said the attacker's motives were still unknown.
The attack comes as France is under a constant threat from terrorism. A string of jihadist attacks have claimed the lives of over 245 people around France in the past three years.
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