Residents said the attackers later left the city and stormed another area some 40 kilometres (25 miles) away, where they burned homes.
The violence prompted the state governor to impose an around-the-clock curfew.
Witnesses said the extremists stormed the city at around 9:00 am (0800 GMT) and advanced without any resistance from the security forces. It was unclear if there were casualties.
A Nigerian fighter jet encircled the city but did not appear to attack the insurgents, said witness Kabiru Na-Gwandu, adding that he had received a call from friends outside of Gombe warning him the gunmen were on their way.
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The Boko Haram fighters called on residents to boycott elections which had originally been planned to take place today before they were postponed until March 28.
"Whoever professes Islam should distance himself from polling stations because we are going to attack polling booths," read the Boko Haram leaflets.
Residents said the gunmen in military uniforms who invaded the city in around 30 vans and on several motorcycles later withdrew from the city unchallenged.
He said fleeing residents of Dadin-Kowa were taking refuge on hilltops from where they could see Boko Haram gunmen burning their homes.
Soldiers were said to be patrolling the streets of Gombe and firing indiscriminately following the withdrawal of the insurgents.
"It is flying bullets everywhere. Soldiers are just firing anyhow. A bullet pieced the wall into my kitchen but luckily we were sheltering in the bedroom," said a journalist in the city.
Two weeks ago, two suicide bombers blew themselves up outside a stadium, just minutes after President Goodluck Jonathan had left the venue where he had given a campaign speech. Many people were injured.