"The body has not yet been examined for identification, but information and clothing are in accordance with the missing woman's," the police write on their website.
The woman, in her 25s, disappeared after a walk in the evening on 13 February and was reported missing on 14 February.
A man in his 40s is in custody, suspected of the act.
The suspicion has until the discovery of the body concerned kidnapping, but is now changed to murder.
"This can not be ruled out at the moment," the police write.
The body was found on Saturday by volunteer divers in the river Nossan.
The dives were done after a private person's dog marked the place.