The unidentified woman in the central British Columbia town of Fort St. John called the Royal Canadian Mounted Police when she spotted the ad in an online buy-and-sell site, the Canadian Broadcasting Corp. reported.
RCMP Sgt. Steve Perret told the broadcaster the ad had been removed this week and electronic forensic investigators had a suspect.
"To me, this looks like a case of somebody's twisted or perverted sense of humor, by posting these types of ads trying to sell somebody else's child," he said. "Additionally there was an ad where he was trying to sell a dead dog."
The woman had posted pictures of her baby on Facebook, which were copied for use in the ad, the CBC said.
Perret said the mother hadn't adjusted her Facebook privacy settings, meaning anyone could view her online wall.
"Unfortunately, all too often people put too much information on the Internet, which can result in things like identity theft," he said.