The suspect was detained near his home and is a former employee of the home for Roman Catholic Missionaries near Montpellier.
A 54-year-old linen maid was killed after a man armed with a knife and a sawn-off shotgun burst into the home in Montferrier-sur-Lez on Thursday evening.
The body of the victim, who had been stabbed, was found gagged and tied up outside the property, according to police.
More than 100 police officers went to the facility, which is home to about 70 men and women who have served as missionaries in Africa.
It was reported that armed officers searched the building room-to-room before leading people to safety, including some who are over the age of 90.
Montpellier prosecutor Christophe Barret said investigators had found a car near the scene of the crime that contained a replica firearm and other materials that enabled them to identify the suspect.
The motivation for the attack is unknown but authorities say there is no apparent link to terrorism.
France has been on high alert in the wake of a series of terror attacks, including the murder of an 86-year-old priest near Rouen in July.