Investigators have not yet taken the mother, 38, into custody, but she and the father both face criminal charges in connection with the case.
Investigators suspect the 43-year-old father and the mother "decided to sell the baby from the start and the woman got pregnant for that purpose", Spanish police said in a statement.
The father is believed to have travelled to Romania before the birth to wrap up the sale with buyers "he was in contact with via Internet."
Police did not say when the arrest or the alleged crime occurred.