People fled into bushes as gunfire rang out in the town, they added.
Boko Haram has changed tactics in recent months by holding on to territory rather than launching hit-and-run attacks.
The government called on Nigerians not to lose hope.
The military was committed to defending Nigeria’s territorial integrity, it said.
Soldiers killed 50 militants during a raid on their hideout in the small north-eastern town of Kawuri at the weekend, the army said.
Last month, Boko Haram said it had established an Islamic state in areas it controls in north-eastern Nigeria.
Michika is a trading centre in Adamawa state not far from the Cameroon border.
Concern is mounting that the group plans to target Maiduguri, capital of neighbouring Borno state, says the BBC Hausa Service’s Bilikisu Babangida.
Thousands of people who have fled towns and villages captured by Boko Haram are taking refuge in the city, which has a population of about two million.
The fall of Michika will add to the fear and panic that has gripped the north-east, as it shows Boko Haram is gaining territory not only in their heartland of Borno but also in Adamawa state, our reporter says.
Amid fears that Boko Haram could advance further into Adamawa, the university in Mubi town has shut, she says.
On Thursday, the militants captured the small town of Gulak after earlier seizing Madagali, which borders Adamawa and Borno states.
Residents told the BBC that Boko Haram fighters entered Michika on Sunday in a convoy of vehicles.
A military jet circled over the town, causing the militants to hide in people’s homes, they said.
There was confusion as people ran into the bush fleeing gunfire, residents added.
It was unclear who opened fire as the insurgents often wear uniforms similar to the Nigerian soldiers, they said.
Last year, President Goodluck Jonathan imposed a state of emergency in Borno, Adamawa and Yobe states, vowing to send more troops to crush the insurgency.
However, Boko Haram has stepped up its offensive since then.
In April, the militants captured more than 200 girls from a boarding school in the town of Chibok, also in Borno state.
Countries such as China, France, the UK and US have sent military assistance to help find the girls but they have not yet been rescued.