The advertisement was posted on the classified website Thursday night, according to the Santa Clarita Valley sheriff's station.
According to CBS Los Angeles, a concerned citizen notified the station about the ad, which said, "Just can't take it anymore. Need to let her go. Her cost is just too much for me and my girlfriend. She's only eight months old, shots are up to date. To a loving home. Call Joshua."
"We're trying to determine who put the ad on, and whether or not there's any validity to the content of the ad," said Sgt. Jeff Curran.
CBS Los Angeles called the number listed on the post, which is now inactive, but it went straight to voicemail.
Detectives said if the situation is a hoax, the person responsible could face misdemeanor harassment charges.
If it's a legitimate ad, the culprit could be charged with child neglect.
"If it is a hoax, somebody thought it was funny when they did it, but we don't consider it funny in any way," said Curran.