Mir Mohammaed Morshed, a spokesman for the state-run Bangladesh Telecommunications Company Ltd., says the government blocked YouTube late Monday.
He says the decision will remain effective until further notice.
On Sunday, the chief of the Bangladesh Telecommunication Regulatory Commission said the government sent a letter to Google, which owns YouTube, urging it to remove the video.
Prime Minister Sheikh Hasina made the same request.
Google has blocked access to the video in Libya and Egypt following violence there, and in Indonesia and India because it says the video broke laws in those countries.
Bangladesh is a Muslim-majority nation of 160 million people but is governed by laws based on British common law.