Foreign ministry spokesman Md Shameem Ahsan told bdnews24.com that Madani arrived at Hazrat Shahjalal airport on a Etihad flight at 7.40am on Sunday.
Foreign Secretary Md Shahidul Huq received him at the airport, Ahsan said.
Earlier the Secretary General was scheduled to arrive on Saturday evening, but his flight had been rescheduled.
The foreign ministry did not cite any reasons for the flight rescheduling.
The OIC Chief is leading a five-member delegation in his first Bangladesh visit after taking office.
A former minister of Saudi Arabia, he assumed office as the tenth Secretary General of OIC on Jan 1 after his election in the 12th OIC Summit in Cairo in February last year.
The foreign ministry said Bangladesh was among the first few countries that he had decided to visit after taking charge of the second largest international organisation.
He is expected to call on Md President Abdul Hamid, Prime Minister Sheikh Hasina, Finance Minister Abul Maal Abdul Muhith, Foreign Minister AH Mahmood Ali, Education Minister Nurul Islam Nahid, and Foreign Secretary M Shahidul Haque.
He will also visit some institutions.
OIC was established through a decision of the Summit in Rabat, Kingdom of Morocco on Sep 25 in 1969 in response to an act of criminal arson of Al-Aqsa Mosque in occupied Jerusalem in Palestine.