The photograph, which shows an adult hand holding the lit cigarette to the baby's mouth, was uploaded to the popular photo-sharing site Instagram.
The photograph has amassed over 2,600 likes and over 36,000 comments since it was posted in January.
The photo was uploaded by Instagram user lapelirrojah_delbarriooh, from Valencia, with the caption "already smoking at a year old, love you little one, you're my fucking life."
Antonio Nieto, vicepresident of the Spanish Association of Pediatricians, has called the photo "absolutely terrible".
"Tobacco is intrinsically even worse than heroin and to give it to a baby whose lungs are still developing," he told The Local.
"Even children who are exposed to passive smoking are more likely to develop lung conditions such as asthma or chronic bronchitis," he added.
For Nieto, giving a baby a cigarette constitutes child abuse:
"I think the police would definitely consider it to be child abuse," he said, "it is just absolutely unbelievable."
The photo has provoked controversy on Instagram and Twitter, where users have slammed the woman who posted the photo; it is unclear whether or not she is the child's mother.
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"You're the worst and you're proud of how stupid you are!" said Twitter user Eli_parra.
Many instragram users have called for the police to investigate the case of "bad parenting".