French police have arrested the mother of a 10-year-old-boy whose body was found stuffed into a suitcase outside Paris, prosecutors said.

The body was found Thursday in the town of Ferrieres-en-Brie - east of Paris.

The mother, aged 33, who police had been searching for since her partner signalled his alarm, was detained in the nearby town of Choisy-le-Roi at the home of a family member, regional prosecutors said.

Concern had initially been triggered after blood was found at the family home and authorities immediately started a search operation.

The investigations led to the discovery of the body of the child "hidden in a suitcase on wheels, in a rubbish bin" close to the family home, said Laureline Peyrefitte, the public prosecutor from the town of Meaux.

"He had several serious wounds, most likely caused by a stab," she added. An autopsy has been ordered to determine the exact causes of death.