One suspect has been arrested.
The area in eastern Paris remained cordoned off by police two hours after the attack.
Children were being sequestered in nine schools while police worked to determine no other suspects were on the run, according to education and police officials.
It is unclear what motivated the attack or whether it was linked to Charlie Hebdo, which moved after its offices were targeted in a 2015 Islamic extremist attack that left 12 people dead.
Police cordoned off the area, including the former Charlie Hebdo offices, after a suspect package was noticed nearby.
But the package was found to be harmless and no explosives were found, according a police official.
An investigation was opened into “attempted murder in relation with a terrorist enterprise”, according to an official at the prosecutor’s office.
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
Authorities did not release the identity of the suspect arrested in the area of the Bastille Plaza.
“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 … I cant tell you how many victims there was, I just saw one,” witness Kader Alfa said at the scene.
AP reporters saw officers flooding into the neighbourhood near the Richard Lenoir subway station.
The two people confirmed injured worked for documentary film company Premieres Lignes, according to founder Paul Moreira.
He told BFM television 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.
A Paris police official said while authorities initially thought two attackers were involved, they now believe it was only one person, who was detained.
The official said police were still searching the area while they questioned the arrested suspect.
Police initially announced four people were wounded in the attack but the official said there are in fact only two confirmed wounded.
They did not release the identities of the attacker or the wounded, who are in “absolutely urgent” condition, the official said.
Prime Minister Jean Castex cut short a visit to a suburb north of Paris to head to the Interior Ministry to follow developments.
The trial in the Charlie Hebdo attacks is currently under way in the city.
Murmurs broke at the terrorism trial of 14 people accused of helping the attackers in the January 2015 killings as the news filtered through.
The widows of the Charlie Hebdo attackers are scheduled to give evidence on Friday afternoon.