The National Emergency Management Agency (NEMA) said the attacks took place at about 20:45 on Sunday close to the Dalori camp at Kofa village, near the Borno state capital Maiduguri.
NEMA northeast region spokesman Abdulkadir Ibrahim said two female suicide bombers tried to get into the camp but were thwarted by security personnel.
"Two other female suicide bombers also detonated their explosives at the adjoining Dalori Kofa village, where they killed 16 people," he added in a statement.
Earlier tolls given by local people said at least 12 or 13 people had been killed but Abdulkadir said three of those injured and taken to hospital had since died.
"The 16 does not include the bombers," he told AFP.
Sporadic hit-and-run attacks
Dalori is about 10km southeast of Maiduguri and is one of the largest camps for internally displaced people (IDP) in the remote region.
Boko Haram has previously tried to target the camp: at least 85 people were killed in January last year when insurgents rampaged through communities near Dalori.
Residents were shot and their homes burned down while female suicide bombers blew themselves up among the crowds of people fleeing the violence.
The latest attack is the most deadly in Nigeria since June 8, when 11 people were killed in a rare combined gun and suicide attack in the Jiddari Polo area of Maiduguri.
Boko Haram has repeatedly targeted the strategic city, particularly its outlying communities, IDP camps and the city's university.
The bombings and sporadic hit-and-run attacks underline the threat still posed by the jihadists, despite claims from the authorities they are a spent force.
Gunmen killed eight members of a civilian militia force assisting the military on June 11 in the Konduga area, which is on the same road as the Dalori camp.
At least 20 000 people have been killed in the conflict since 2009 and more than 2.6 million made homeless, many of whom are facing severe food shortages or starvation.