Military TV said a state of emergency had been declared for one year and power transferred.
The coup comes after tensions rose between the civilian government and the military following a disputed election.
Myanmar, also known as Burma, was ruled by the military until democratic reforms began in 2011.
The military said on Monday it was handing power to commander-in-chief Min Aung Hlaing because of "election fraud". Soldiers are on the streets of the capital, Nay Pyi Taw, and the main city, Yangon.
In November's election, Ms Suu Kyi's National League for Democracy (NLD) won enough seats to form a government.
The United States has condemned the coup, saying Washington "opposes any attempt to alter the outcome of recent elections or impede Myanmar's democratic transition".
US Secretary of State Antony Blinken called for the release of all government officials and civil society leaders and said the US "stands with the people of Burma in their aspirations for democracy, freedom, peace, and development. The military must reverse these actions immediately."
In Australia, Foreign Affairs Minister Marise Payne said "we call on the military to respect the rule of law, to resolve disputes through lawful mechanisms and to release immediately all civilian leaders and other who have been detained unlawfully."