Tadesse Ayalewe, deputy commissioner at the federal police's Corruption Crimes Investigation Office told the broadcaster Mitiku Kassa was suspected of conspiring with a head of an NGO called Elshadai.
The charity received food and clothing that were purportedly intended for displaced persons, and these were then sold "to buy a residential house for the suspect," Tadesse said.
The arrest was carried out after police conducted extensive surveillance on the suspect, he added.
NDRMC Commissioner Kassa, who has run the public body since 2015, had previously been state minister for disaster risk management and food security.
In December 2019, he was also appointed as a member of the UN Secretary-General's High Level Panel on Internal Displacement.
Meanwhile, Ethiopia is facing a major humanitarian crisis sparked by conflicts and drought.
With nearly five million people displaced, a total of 26 million Ethiopians -- almost a quarter of the population -- need emergency food aid, according to the United Nations.