A woman who saw the offer on the popular website alerted police who tracked down the 23-year-old mother and 26-year-old father using a cell phone number that was listed in the advertisement.
Vancouver police said the couple told investigators the offer was a hoax, but were arrested for public mischief with other criminal charges possible as the investigation continues.
"There are so many questions here," Constable Tim Fanning told reporters.
Police said the advertisement described the baby as "very cute" and "unexpected" and that its parents, who could not afford to care for it, wanted to give it a good home.
The child was put in the care of social workers.