Latifa Bourkri, 24, was reported missing on January 6th at around 6.30pm, cantonal police said.
As far as police know her husband was the last person to see Bourkri, although she had left him on December 13th when she took up residence in a women’s shelter in the city of La Chaux de Fonds.
The separation occurred came not long after the couple was married in June 2014 and moved into a home in the watch-making city in October, police said.
Local prosecutor Daniel Hirsch has opened an investigation into kidnapping against the husband who has been placed in detention.
“Some surprising factors have appeared and this individual became a suspect,” Hirsch is quoted as saying by 20 Minutes newspaper.
“All the same he denies any involvement in this disappearance.”
Police said the husband was driving a white Nissan Qashquai with Neuchâtel licence plates NE 117759.
The missing woman, described by police as “the victim”, was using a black Renault Mégane with French licence plates AP-622-KY (68).
The woman has not been in contact with other members of her family since January 6th, police said.
Police are looking for any information or observations regarding the man and woman or their cars.
Anyone with such information is asked to phone 004 132 8899000.