Military-controlled state and media companies will also be blocked from the two social media platforms, while army-linked commercial firms will not be able to run advertisements.
The ban does not affect government ministries and agencies that provide essential public services, such as the health ministry and the education ministry, the social media giant said.
Myanmar's army seized power on Feb. 1, after arresting members of the democratically elected government, including Nobel Laureate Aung San Suu Kyi. The military claimed there was voter fraud in last year's election and declared a one-year state of emergency.
Thousands of people have protested the coup, and clashes with authorities have sometimes turned violent. Reports say at least three protesters and one policeman have died so far.