The minister was tested for the coronavirus as part of a routine check-up ahead of his trip to Niger for the 47th Foreign Ministerial Conference of the Organization of Islamic Cooperation (OIC), the foreign ministry said in a statement on Wednesday.
The result later came back positive on Tuesday.
Momen did not display any symptoms of the coronavirus at the time, according to the ministry.
The minister's visit to Niger has now been cancelled. He is currently isolating at home following doctor's advice and is in good health.
Momen was scheduled to attend the OIC conference as the leader of the Bangladeshi delegation.
A team comprising officials from the Ministry of Foreign Affairs and the Bangladesh Embassy in Riyadh, Saudi Arabia, in coordination with Permanent Mission of Bangladesh will now represent the country at the conference.
Meanwhile, Foreign Secretary Masud Bin Momen also tested positive for COVID-19 ahead of the visit to Niger. He, too, is in isolation at home and is healthy.