On Friday, TV footage showed ambulances, fire trucks and police cordoning off the area around Charlie Hebdo's former offices.
Paris police said two people were "critically wounded" in Friday's attack, which is being investigated by specialist anti-terror prosecutors.
It is unclear what motivated the attack or whether it had any link to Charlie Hebdo, which moved offices after they were attacked by Islamic extremists in 2015, who killed 12 people inside.
The man was detained near the sprawling Place de la Bastille, police said, adding he was the only suspect in an attack.
Police initially reported four people had been injured in the stabbings and two assailants were on the run but they have since revised the figures downwards with no explanation given.
The area in eastern Paris remained cordoned off by police two hours after the attack.
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One police source said a machete had been found at the scene. The widows of the Charlie Hebdo attackers are scheduled to testify Friday afternoon. (AP Photo/Thibault Camus) Police did not release the identities of the attacker or the wounded, who are in "absolutely urgent" condition, the official said.
Local authorities have asked people to avoid the area after a suspicious package was spotted, however, no explosives were found in the suspicious package near the scene, officials said.
"A serious event has taken place in Paris", said Prime Minister Castex, who was addressing reporters at the time and cut short a visit to northern Paris to head to the crisis centre at the interior ministry.
But after several high-profile attacks in recent years, DW's Paris correspondent Lisa Louis said France was still on edge.
The trial of alleged accomplices in the 2015 attack began in Paris earlier this month. The threats coincide with the trial of 14 suspected accomplices of the perpetrators of the massacres at Charlie Hebdo and a Jewish supermarket that left a total of 17 dead.
A police operation was in force in the northeastern district of Paris near the former offices of Charlie Hebdo.