The selfie-style video was filmed on November 5, according to the office of State Counselor Aung San Suu Kyi, and after it was posted to YouTube on Saturday, quickly went viral.
It's the first time the government has announced an investigation into police brutality against the Rohingya ethnic minority in the restive Rakhine State since the area was put under lockdown following an attack on border guards in October.
Nobel laureate Aung San Suu Kyi has been accused of turning a blind eye to the Rohingya minority.
In an interview with CNN in September, Suu Kyi said her government was having "a lot of trouble trying to bring about the kind of harmony and understanding and tolerance that we wish for."
"This is not the only problem we have to face, (but) this is one on which the international community has focused," she added.
Speaking to CNN, former US Ambassador to Myanmar Derek Mitchell said Suu Kyi is "under enormous stress."
"It's unclear how much she knows about what's going on on the ground," he said, adding that the international community should consider the "context of decades if not centuries of mistrust" of Rohingya by the majority population in Myanmar.
However, he said that Suu Kyi "does need to step up and do more to speak to the urgent immediate issue of the human rights of these people."
Myanmar's government has been accused
of reacting to October's attack with further violence. Officials have consistently denied human rights abuses, saying they are carrying out "clearance operations" against those involved in the attack.
Series of videos
"It's telling that these local officers apparently felt so at ease in what they were doing that they had no hesitation in filming it," Phil Robertson of Human Rights Watch told CNN.
"If the police feel so immune that they film themselves inflicting such brutal beatings, one wonders what other horrors might be taking place off camera that they were not willing to record."
This is the latest in a series of videos that show alleged abuse by Myanmar authorities in recent months. Another video
from November shows burned bodies and the remnants of a burned house. Human Rights Watch said that hundreds of homes have been destroyed as part of the crackdown.