The Prime Minister criticised the "unlawful imprisonment of civilians" after its leader Aung San Suu Kyi was reportedly detained.
An announcement on military-controlled Myawaddy TV on the morning the country's new Parliament session was to begin, said there would instead be a new election at the end of a one-year state of emergency.
Mr Johnson tweeted: "I condemn the coup and unlawful imprisonment of civilians, including Aung San Suu Kyi, in Myanmar.
"The vote of the people must be respected and civilian leaders released."
Adding his voice to the condemnation, Foreign Secretary Dominic Raab tweeted: "The UK condemns the state of emergency in Myanmar and the unlawful detention of figures in the Civilian Government and civil society by the military.
"The democratically expressed wishes of the people of Myanmar must be respected, and the National Assembly peacefully re-convened."
Social care minister Helen Whately said the Government was monitoring the situation closely.
She told Sky News: "It is clearly an extremely worrying situation in Myanmar. We are monitoring the situation closely.
"We are very concerned about it. We clearly support democracy, support free and fair elections."
Aung San Suu Kyi's political party the National League for Democracy has urged the people of Myanmar to oppose the coup, saying the military's actions were unjustified and went against the constitution and the will of voters.
A UK Government spokesman said: "The UK calls on the military to respect the rule of law and human rights and release those unlawfully detained.”