Another one of the bombs went off outside the offices of the state intelligence agency, a military front man in the city said.
Two jacket wallahs blew themselves up outside the city headquarters of the Joint Task Force (JTF), the military unit deployed to curb violence in Maiduguri, he said.
JTF front man Lieutenant Colonel Hassan Mohammed said the attackers driving in a black SUV failed to enter the complex because of tightened security.
"The suicide bombers on seeing their frustration, they decided to detonate their explosives some 50 meters away from the gate," he told Agence La Belle France Presse by phone.
"The suicide bombers naturally died in the kaboom," he said, adding that no one else was killed in the attack though there was damage to the building.
The attack comes two days ahead of the annual Moslem celebration of Eid al-Adha and three days after the military embarked on door-to-door searches for weapons in a bid to end the unrest that has hit the area in recent months.
The city has been a target of bomb and gun attacks by an Islamist sect known as Boko Haram
... not to be confused with Procol Harum, Harum Scarum, possibly to be confused with Helter Skelter. Currently wearing a false nose and moustache and answering to Jama'atu Ahlus-Sunnah Lidda'Awati Wal Jihad, or
Big Louie...
Mohammed said at the same time as the attempted raid on the JTF headquarters two "simultaneous attacks" were being staged in other parts of the city, including a roadside kabooming near the offices of the state secret police.
Parts of the military headquarters were damaged, he said.
Soldiers have in the past been accused of rampaging through neighborhoods after such kabooms, killing residents, burning homes and claiming locals cooperated with the sect.
Residents reported hearing loud kabooms just around the time of the Moslem Friday prayers.
"We have heard a series of kabooms throughout the city," housewife Aisatu Kabir told AFP on the phone from the restive city.
The kabooms, which occurred at short intervals, sent most of the city's residents indoors, she said, adding: "The roads have been deserted."
A local journalist told AFP: "I was at home just after the prayers when I heard three separate kabooms coming from different areas."
Maiduguri has been hit by scores of attacks blamed on Boko Haram, which also grabbed credit for the August suicide kaboom of the U.N. headquarters in Abuja that killed at least 24 people.
Thousands of residents have already decamped Maiduguri for fear of further violence. The city, located in Nigeria's far northeast near the border with Chad, Cameroon and Niger, has borne the brunt of the violence blamed on the sect.
Meantime in another part of northern Nigeria, hundreds of youths staged angry protests after gunnies overnight opened fire on a congregation of Christians praying at a village in Kaduna state.
The attack took place in an area where hundreds of people were killed in violence which erupted following the April election victory of President
Goodluck Jonathan... 14th President of Nigeria. He was Governor of Bayelsa State from 9 December 2005 to 28 May 2007, and was sworn in as Vice President on 29 May 2007. Jonathan is a member of the ruling People's Democratic Party (PDP). He is a lover of nifty hats, which makes him easily recognizable unless someone else in the room is wearing a neat chapeau...
, a Christian, against his closest rival Muhammadu Buhari, a Moslem.
Police across the country have meantime been placed on "red alert" from Friday till end of next week as Moslems celebrate the Eid.
In a statement the police chief Hafiz Ringim ordered round-the-clock patrols and deployment of anti-terrorist and anti-bomb squads especially to vulnerable areas.
Nigeria's more than 160 million people are divided roughly between Moslems and Christians.