Junedin Basha said the East African country decided against running as the replacement for Libya after meeting with Confederation of African Football officials.
CAF wants a country with already-established facilities to step in at short notice for 2017 after Libya withdrew as host in August because of security and organizational concerns. Ethiopia's bid revolved around building new stadiums.
CAF executives "advised" Ethiopia to delay its bid, Junedin said.
Zimbabwe and Algeria say they have submitted formal bids to host the 2017 tournament, while other candidates could include Ghana, Kenya, Tanzania and Egypt. The deadline for bids to be lodged was Tuesday.
Morocco will stage the next 16-team African Cup in January and February. Cameroon, Ivory Coast and Guinea have been named as hosts for 2019, 2021 and 2023 respectively.
CAF said it will name the 2017 host early next year.
The Associated Press.