The manager of a refugee centre in the city of Pau, south-west France, was killed on Friday in an attack allegedly carried out by a Sudanese migrant.
The stabbing happened at about 11:00 local time (10:00 GMT) and the suspect has been arrested.
Interior Minister Gérald Darmanin said on Twitter he would travel to the city later on Friday.
Reports in French media suggest the attacker was a 38-year-old man who had previously lived at the centre.
Police sources, cited in French media, suggest he had recently had his refugee status rejected by French immigration services.
The attacker was previously known to the police and the incident is not thought to be linked to terrorism, the AFP news agency reports.
The victim, 46, has not yet been named.
Mr Darmanin said he would meet officials at the centre on Friday and he offered his “sincere condolences” to the victim’s family and loved ones.