Ban said the support should be provided with the backing of the AU and the Multinational Joint Task Force, to defeat the terrorist group.
He condemned the suicide attack that took place on Wednesday in the far North region of Cameroon.
The UN chief reiterated that no cause can justify terrorist attacks.
The Secretary-General expressed his deepest condolences to the families of the deceased and to the government and people of Cameroon and wished a speedy recovery to those injured in the attack.
According to Cameroonian authorities, on the evening of Wednesday, six people were killed when a young boy detonated a bomb in Djakana, a district of the town of Limani in northern Cameroon, near the Nigerian border.
The bomber died on the spot while five people who were wounded during the attack later died in hospital.
According to Amnesty International, from July 2015 to date, Boko Haram has conducted at least 200 attacks, including nearly 40 suicide bombings in the far north region of Cameroon, which have killed at least 480 people.
Boko Haram launched its first such attack in Cameroon on July 12 2015, in Fotokol, killing 13 civilians and two soldiers.