A man arrested for allegedly attacking a woman with a box cutter shot and seriously wounded two officers in a Paris police station on Thursday after grabbing one of their weapons.

A source close to the case said the incident happened in the French capital's 13th district shortly before 10:30 pm (2030 GMT), and that one of the officers' wounds were life-threatening.

The Paris public prosecutor's office later confirmed the source's account to AFP.

Paris police chief Laurent Nunez arrived at the scene around midnight, accompanied by prosecutor Laure Beccuau.

Nunez told reporters that the suspect had been arrested at around 10:00 pm for a "very violent attack on a woman" with a box cutter.

"The officers intervened and brought him back here (to the police station), and it was during his processing that he snatched the weapon" and "seriously" wounded the two officers, he said.

The officers were both immediately transferred to hospital, as was the suspect, who was himself seriously wounded by return fire, Nunez added.

"We are very worried about the state of health (of the officers)," he continued, lauding the station staff's "courage and responsiveness".

Nunez said an investigation was underway to establish the "circumstances" surrounding the incident.

Reached by AFP, the prosecutor's office said three investigations had been opened -- one into the "attempted murder of the woman", and one into the "attempted murder of persons holding public authority".

The third was being carried out by the IGPN, the national police's internal affairs department, to look into the use of "intentional violence with a weapon by a person holding public authority", as is routine when an officer uses their weapon.

The office said the suspect had been hospitalised with a chest wound, but his life was not in danger.

"The investigations should clarify the circumstances of the events, the identity of the suspect and his possible links to the female victim," it added.