"No one has the right to take pictures of someone and publish them without his permission," Dubai police chief, Khamis al-Mazeina, was quoted as saying by the daily Emiratalyoum.
He said the Asian video maker was arrested following a complaint by the family of the Emirati man.
The footage of the beating shows a man of small posture, dressed in a traditional white Thawb, attacking the Indian driver of a delivery van following a minor car accident in Dubai.
Media reports said the attacker had also been arrested after the video surfaced online, although the victim of the assault lodged no complaint with the authorities.
The UAE is home to millions of foreigners, mostly from South Asian countries.