National Emergency Management Agency, said the blasts happened at about 11:20 pm (2220 GMT) on Sunday.
Abdulkadir Ibrahim, from the National Emergency Management Agency, said the blasts happened at about 11:20 pm (2220 GMT) on Sunday, just outside the Borno state capital of Maiduguri.
"Two suicide bombers (a male and a female) detonated their improvised explosive devices at Dalori 1 IDP (internally displaced persons) camp, leading to the death of three IDPs, while 17 others were injured," he said in a statement.
"Another incident occurred at Dalori 2 IDP camp, where a suicide bomber was intercepted, leading to the death of the suicide bomber."
Ahmed Sartori, the head of the Borno state emergency management agency, said the death toll had risen by late morning.
"The death toll is now four, with the death of one more victim," he told AFP, adding that another suicide bomber had died trying to get into the city's university.
"A suicide bomber exploded while he was trying to scale the barbed wire fence at the university," he said.
A trench is currently being dug around the campus, which lies on the edge of Maiduguri, to deter intruders after a spate of suicide bomb attacks on the premises.
The Islamist militant group Boko Haram has increasingly used suicide bombers in its eight-year insurgency that has left at least 20,000 dead and displaced more than 2.6 million others.
Dalori, which is about 15 kilometres (nine miles) from Maiduguri, houses some 50,000 people in makeshift accommodation and has been targeted by bombers before.
On the evening of June 18, two women blew themselves up at Dalori 2, where 10,000 people are living, The attack injured several IDPs but killed only the bombers.
It followed a separate attack at nearby Kofa village, where two women used as human bombs exploded, killing at least 16.
On January 30 last year, at least 85 people were killed when militant fighters stormed and torched Dalori village and tried to gain access to the IDP camps.
Nigeria's military and government maintain the jihadists are a spent force after a sustained counter-insurgency pushed them out of captured territory since early 2015.
But signs remain that the violence is far from over. On Sunday, police in the northern city of Kano said they had arrested five Boko Haram members after a gunfight.
Kano state police chief Rabiu Yusuf said the three men and two women were suspected of planning attacks on markets and places of worship.
The city has seen a lull in Boko Haram activity since a November 2014 gun and suicide attack at the main mosque killed more than 100.
An internal army memo, seen by AFP, also indicated Boko Haram was back in its "Camp Zero" enclave in the Sambisa Forest of Borno, which had been declared cleared in December last year.
Nigeria's highest-ranking army officer, Lieutenant General Tukur Buratai, has ordered troops to capture Boko Haram's leader Abubakar Shekau "dead or alive" within 40 days.
The authorities have previously declared the elusive Shekau dead on a number of occasions, only for him to reappear in video messages.
Yan St-Pierre, the head of the Modern Security Consulting (MOSECON) group and a counter-terrorism advisor, told AFP the chief of army staff's order was "more rhetoric than fact".
"The Nigerian Army needs a boost and even if unsuccessful the ultimatum is nonetheless a reminder that (it) needs a big result and some form of success needs to be delivered," he said.
Africa security specialist Ryan Cummings suggested the time-frame could coincide with the end of the rainy season in October to prevent greater Boko Haram movement.
Politics could also be behind the statement, said St-Pierre, with President Muhammadu Buhari on indefinite sick leave and under pressure to ease public concerns about his health.