Hours after the arrests, military TV confirmed a state of emergency had been declared for one year.
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. 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 army says the vote was fraudulent.