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.