At least 44 people were killed when Dumba, a Nigeria-Chad border community near Baga, a town close to state capital Maiduguri, was attacked by the militants last Tuesday, Xinhua reported.
NEMA spokesperson Abdulkadir Ibrahim said in a statement that the 4,000 displaced people include mostly women, children, fishermen and farmers.
All displaced victims of the attack stayed at a public school in Baga, said the spokesperson.
"The internally displaced persons were provided with mattresses, blankets, mosquito nets, and other non-food items like buckets, cups, plates, wax prints, toilet soaps, sanitary pads and detergents," the official added.
Food items including rice, maize, guinea corn, millet, vegetable oil, palm oil, noodles, salt, sugar and milk, were also distributed.
Ibrahim said that Red Cross and other rescue agencies and health officials are providing assistance to the displaced people.
Victims of the attack said the attackers stormed their community, slitting the throats of residents and shooting sporadically. Houses were burnt and many villagers were injured.
Boko Haram, based in northeastern Nigeria, seeks to enshrine the Islamic sharia law in the constitution, declaring war against Western education.
Amid increasing casualties including women and children, President Goodluck Jonathan tried but failed to reach a cease-fire with the sect in April.