A suspect was arrested in the neighboring Bastille district. A second suspect has also been arrested, according to reports.
The counterterrorism police have resumed the investigation.
A security cordon has been put in place in the 11th arrondissement east of Paris. The public were told to avoid the area.
A blade – described as a machete or a meat cleaver – was found at the scene of the attack near Boulevard Richard Lenoir.
One of the arrested suspects was detained with blood on his clothes, a police source told the BBC.
Initial reports indicated that four people had been injured.
The attack comes amid a high-profile trial underway in Paris against 14 people accused of helping two jihadists carry out the 2015 attack on Charlie Hebdo, in which 12 people were killed.
The two injured were staff members of a television production company, one of their colleagues told AFP news agency.
“Two colleagues were smoking a cigarette outside the building, in the street. I heard screams. I went to the window and saw a colleague of mine, covered in blood, being chased by a man with a machete in the street, ”another staff member of the production company First Lines.
The firm has offices in rue Nicolas Appert, a side street of boulevard Richard Lenoir where the former offices of Charlie Hebdo are located.
The satirical magazine has since moved to a secret location.
Charlie Hebdo marked the start of the trial by reprinting controversial cartoons of the Prophet Muhammad that sparked protests in several Muslim countries.
The defendants at the trial are also accused of aiding another jihadist in a related attack in which he shot a policewoman and then attacked a Jewish store, killing four people.
All 17 victims were killed over a three-day period. The three attackers were killed by the police. The killings marked the start of a wave of jihadist attacks across France that left more than 250 dead.