The attack happened in Dikwa, some 90 kilometres from the Borno state capital, Maiduguri, yesterday morning and is believed to be a reprisal for a military strike on Boko Haram strongholds in the area last week.
It will again raise security fears about the safety of internally displaced people (IDPs) and put pressure on the government, which maintains it has the upper hand against the insurgents and is pushing for the return of civilians caught up in the violence.
He promised those behind the attack would be hunted down and ordered that "formidable security in and around the IDP camps in the country be beefed up and renewed measures put in place to guard against future occurrences".
The head of the Borno State Emergency Management Agency, Satomi Ahmed, earlier told AFP 35 bodies were recovered from the camp, which houses some 53,600 people, with 78 injured.
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"From what we gathered three female suicide bombers disguised as IDPs arrived at IDP camp at about 6.30 local time ," he said.
"Two of them detonated their explosives. The third one refused to set off hers when she realised her parents and siblings were in the camp. She surrendered herself to the authorities."
Ahmed said the woman told the military why she refused to detonate her explosives and warned them of further attacks to come in the remote region.
The injured were taken to the Borno State Specialist Hospital and the Umaru Shehu Hospital, both in Maiduguri for treatment, he added.
Last week, the Nigerian military attacked three villages considered Boko Haram strongholds near Kalabalge, killing dozens of militant fighters and rescuing hundreds of women.