They had fled across the border to Bangladesh amid heavy fighting between the Myanmar military and rebel insurgents in Rakhine
Abdus Salam, member of Kajalshah Union Parishad, was arrested at Kanaighat along the border with India on Thursday afternoon, police said.
The incident in the video occurred three to four months ago, but no one had complained about it, Additional Superintendent of Police Mahbub Alam said.
The man who was beaten is identified as Gias Uddin Afzal, a resident of Atgram village.
In the 24-second video, Afzal is seen hanging from a bamboo with his hands and legs tied while Salam is canning Afzal with a crowd of onlookers gathered around the place.
Mahbub said they were investigating other complaints of torture against Salam as well.