The priest then holds either side of the child's face and appears to slap the crying baby, raising his voice after he does so.
The woman can be heard saying something to the priest before the man has to physically remove the baby from the priest's arms.
When the inconsolable baby continues to cry, the visibly agitated priest strike him across the face, hard enough to make a clear sound in the clip.
"And then, I'll kiss the little kid - because he'll have become a little Christian".
No further details have been revealed about the family or whether or not the parents pressed charges for the priest's actions, nor has any representative from the Catholic Church released a statement regarding the priests behaviour.
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The priest is shown to hit the poor child in the face because he would not stop crying.
As it carries on crying the priest says: 'Calm down, calm down, you must calm down'. "I was trying to calm him down; I didn't really know what to do".
"He is just a strict old man who thinks he has to be obeyed and does not recognise the strength of his grips", one person wrote.
It's unclear when and where the video was taken.
She then tries to take the child back, but the priest appears to hold the child tighter, with the mum telling him to "Let go, no, no, let go".