The Islamists' assault on the Borno state capital came a day after President Muhammadu Buhari's inauguration, with the new leader vowing to re-enforce Maiduguri with a new command and control centre to better coordinate the counter-insurgency effort.
Shortly after midnight (2300 GMT Friday), residents in the Dala suburb south of the city woke to the sound of RPGs being fired in succession, said resident Modu Karumi, in an account supported by several others.
Witnesses said hundreds of Islamist gunmen were trying to advance on the city, which is now home to hundreds of thousands of people displaced by unrest in other parts of Borno state.
An AFP reporter who lives in the area said he heard what sounded like armoured personnel carriers deploying to the southern edge of Maiduguri to face the rebel advance.
Dala resident Alhaji Bukar said he saw at least one RPG fall into a private home, but details on casualties were not immediately clear.
Locals reported other residential homes being hit.
Three senior security sources in Maiduguri who were not authorised to speak publicly said the attack had been repelled.
"All is under control. There is no cause for alarm," one of those sources told AFP.
The sound of RPGs and gunfire has also eased, residents and an AFP reporter said.
Experts doubt that Boko Haram currently has the capacity to seize Maiduguri, but a major attack inside the city would likely be disastrous for civilians.
The Islamist rebels have been flushed out of several Borno state towns they controlled in an offensive launched in February by Nigeria with backing from neighbouring Cameroon, Chad and Niger.
But there are signs of the militants regrouping, particularly in the remote parts of eastern Borno near the Cameroon border.
Buhari in his inaugural address on Friday vowed to intensify the fight against Boko Haram, notably by shifting operational command from the capital Abuja to Maiduguri.
His predecessor Goodluck Jonathan's performance against the militants was heavily criticised, with the conflict killing more than 15,000 people since 2009 and forcing another 1.5 million from their homes.
Buhari, a former army general, insists the uprising can be defeated and has placed the Boko Haram effort at the top of his administration's agenda.