"I have received with great concern reports of the flooding in Benue state, displacing, from early estimates, more than 100,000 people," Buhari wrote on Twitter late on Thursday.
He said his government "will make available all assistance" to those affected.
"We will surmount this disaster, and, working with the State Govt, bring succour and relief to all affected persons and communities."
Helen Teghtegh, head of local NGO Community Links and Human Empowerment Initiative, said the region had been battered by heavy rains over the past two weeks with the level of the Benue river steadily rising.
Many residents in the state capital Makurdi have fled their homes since Wednesday, she added, launching an appeal for donations.
"We are still trying to get accurate data, we don't know the number of casualties, but we are having a meeting tomorrow with local groups and emergency services, so we should know better," said Teghtegh.
Photographs of inundated Makurdi began spreading on social media on Thursday, showing cars and thousands of homes completely submerged. Others showed men and women carrying mattresses, bags, and other belongings as they fled on foot.
Buhari and his government have faced criticism in the media and online over what many called the inaction of authorities to tackle the flooding.
On Thursday, Buhari said he called for the National Emergency Management Agency to step in.
Two camps have been set up in Makurdi to accommodate those made homeless, but they will not open before the weekend.
Benue state, which is heavily reliant on its agricultural sector, has suffered repeated floods in recent years, caused by heavy rains and the opening of dams in neighbouring Cameroon.
In 2012, Nigeria suffered disastrous floods across 30 of its 36 states. Hundreds of people died, and some two million people were left homeless.