The little girl is seen swaying, apparently intoxicated, while someone firstly puts a beer bottle to her mouth, and then a lit joint.
She then appears to almost fall over and pass out as her mum rushes to catch her.
The mother, 17, and father, 18, were arrested at their home in Formosa in Argentina after the video did the rounds on social media, The Mirror reports. The child was reportedly taken away from her parents, and is now in the temporary care of her grandmother.
According to the parents, the video was made as a joke, and they are claiming they had not really given the child alcohol or cigarettes.
People expressed their horror at the video, with many saying the parents "deserve the worst" and "they aren't parents".