An NYU student was randomly attacked Monday in Greenwich Village ... and now a suspect has been arrested for the bizarre butt-slapping on a sidewalk, TMZ has confirmed.

Watch the video ... a man wearing a light-blue scarf follows a 20-year-old woman across a busy street to sneak up behind her and strike her hard on the behind. He follows up by knocking her to the ground with another vicious blow to the head.

This all took place in broad daylight in lower Manhattan as the poor woman was just trying to make her way to a 9:30 AM class.

The video also shows passersby -- clearly stunned by the occurrence -- tend to the woman after her fall.

Thankfully, the school is on top of it, and so are the police.

NYU spokesperson John Beckman tells TMZ ... "The University is deeply disturbed by the a

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