Two people were hurt in the incidents and French authorities said two suspects have been arrested.
The main suspect had been arrested a month ago on the steps of the Bastille Opera, not far from the attack site, for carrying a screwdriver but was not on the police radar for Islamic radicalisation.
The interior minister said the young man arrived in France three years ago as an unaccompanied minor, apparently from Pakistan, but his identity was still being verified.
The attack happened in front of the building where Charlie Hebdo was based until the Islamic extremist attack on its cartoonists and at a time when suspects in the 2015 attack are on trial across town.
“But manifestly it’s an act of Islamist terrorism,” Interior Minister Gerald Darmanin said in an interview with the France 2 television station.
“Obviously, there is little doubt. It’s a new bloody attack against our country, against journalists, against this society,” he said.
Prosecutor Jean-Francois Ricard said the people hurt were two workers in a documentary production company who had stepped outside for a smoke break and the assailant did not know them.
French Prime Minister Jean Castex said the lives of the two wounded workers are not in danger and offered the government’s solidarity with their families and colleagues.
The suspects’ identities have not been released, and it is unclear exactly what prompted the attack.
Police flooded the area in eastern Paris soon after the attack and cordoned off the neighbourhood.
“All the team at Charlie offers support and solidarity to its former neighbours and colleagues at PLTVfilms and to the people hit by this odious attack,” Charlie Hebdo tweeted.
The prime minister noted the “symbolic site” of the attack, “at the very moment where the trial into the atrocious acts against Charlie Hebdo is under way.”
He promised the government’s “unfailing attachment to freedom of the press, and its determination to fight terrorism.”
The two people confirmed injured worked for documentary film company Premieres Lignes, according to founder Paul Moreira.
He told BFM television that the attacker fled into the subway, and the company’s staff members were evacuated.
Mr Moreira said a man in the street “attacked two people who were in front of the building, didn’t enter the building, and who attacked them with an axe and who left.”
He said the company had not received any threats.
Witness Kader Alfa said: “I saw a guy that was in his 30s or 40s with an axe in his hand who was walking behind a victim covered in blood.”