The shocking video of the scene which happened in an unknown French speaking country has gone viral and has been viewed hundreds of thousands of times.
The ceremony, which is taking place in French, appears to show the child getting more distressed and seemingly annoying the priest.
He grows frustrated and slaps the baby in his face. He then attempts to console the child by grabbing the boy's face and urging him to "calm down, calm down".
"And then, I'll kiss the little kid - because he'll have become a little Christian".
"I don't care if you're a pastor, priest or one of Jesus 12 disciples", one angry viewer tweeted. "If. You".
Onlookers, clearly appalled by what they've just seen can be heard saying, "Sir we don't hit him" and "Isn't this forbidden?"
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Two adults stood at the font, believed to be the young child's parents, are stunned and quickly try to wrestle the child away from the elderly religious man.
The priest was heard saying afterwards: "There, you have to calm yourself, you have to calm yourself, there, there".
Finally, the man believed to be the child's father interjects, and removes the child from the situation before the video cuts out.
While doing this, the priest uttered the words "Calm down", to the dismay of the child's family.
People on YouTube took to the comments section to express their outrage at the priest's behavior.