The commission is the government body that oversees the internet in Bangladesh.
Last month over 70 people, mainly Bangladeshi army officers, were killed in a mutiny by border guards, apparently sparked by poor pay and work conditions, at the Dhaka headquarters of the Bangladesh Rifles.
The insurrection shook the two-month old government of Sheikh Hasina, the prime minister, and raised tensions with the military.
The mutiny ended through negotiations, with Hasina offering amnesty to the border guards.
But when dozens of bodies - including those of 56 officers - were discovered dumped into shallow graves or sewers on the compound, the government rescinded the amnesty for those behind the mutiny.
The clip posted on YouTube was apparently of Hasina defending her decision to negotiate with the mutineers while army officials shouted and jeered, drowning her out and preventing her from speaking.
Military officials and others with knowledge of the meeting said the gathering had been tense.
Nasrin Sultana, a manager at Access Telecom Bangladesh Limited, one of the country's major internet providers, said the site was blocked late on Sunday because of an audio clip from the March 1 meeting.
Officials at Google, YouTube's parent company, could not be immediately reached for comment.
Thirty-six suspects have been arrested in connection with the mutiny, police said on Sunday.
"We're questioning the arrested guards, who are believed to have been involved in the carnage," Abdul Kahar Akhand, an officer of the criminal investigation department, said.
Bangladesh sought technical and forensic assistance from the FBI as well as from Britain's Scotland Yard after the February 25-26 mutiny and on Sunday an FBI team was said to be on its way to Bangladesh to make an initial assessment.