The UN refugee agency and Nigerian authorities have so far registered some 2,000 Cameroonians who have fled into southeastern Nigeria since Oct 1, while another 3,000 were awaiting registration.
Even more people are believed to be trapped in forests on the Cameroonian side, AFP reported.
"We are preparing to help up to 40,000," UNHCR spokesman Babar Baloch told AFP, stressing though that the number of people fleeing into Nigeria could easily surpass that figure.
French-speaking Cameroon has a large Anglophone minority which comprises around a fifth of its population of 22 million.
Gathered mainly in two regions, many English speakers say they suffer inequality and discrimination.
Resentment has fuelled a breakaway movement that on Oct 1 issued a symbolic declaration of independence for the putative state of Ambazonia, prompting a crackdown by President Paul Biya's security forces that left dozens dead and many injured.
UNHCR said it was helping Nigerian aid workers distribute relief items in Nigeria's Cross River State, including 40 tones of food, mattresses, blankets, mosquito nets and hygiene kits.
The agency warned that the new refugee crisis came at a time when Nigeria and Cameroon were already grappling with one of the world's worst humanitarian crises.
Some 2.5 million people in the Lake Chad region have already been displaced by the Boko Haram insurgency, which has killed at least 20,000 people since 2009.
In the latest attack, at least 20 people were killed in a series of attacks in Cameroon and Nigeria on Monday.