The North Africans had requested a postponement because of fears over the Ebola outbreak.
The Confederation of African Football (Caf) refused the request and set a deadline of 8 November for Morocco to confirm they would host the tournament.
The deadline was also given to any countries who may want to step in as replacement hosts.
A statement from Morocco’s sports ministry said: “The decision is dictated by health reasons because of the serious threat of Ebola and the risk of its spreading.”
A judgement on the future of the 2015 tournament is set to be made on 11 November when Caf has an executive committee meeting in Cairo.
Morocco, which last staged the finals in 1988 and which will host Fifa’s Club World Cup next month, had asked for the 16-team tournament to take place in either June 2015 or January 2016.
However, Caf’s executive committee unanimously agreed to maintain the dates of next year’s competition – which is scheduled to run between 17 January and 8 February.
“We will never take any risk if we are unsure about whether a competition poses a threat to the hosts,” Caf secretary-general Hicham El Amrani told BBC Sport on Tuesday.
“That would be as disastrous for us as for any nation having the virus.”
El Amrani said that consultation with the World Health Organisation (WHO) had been key to the rejection of Morocco’s request.
“Their advice was very clear, in that they only recommend cancelling mass gatherings and football matches in the heavily-affected countries: Guinea, Liberia and Sierra Leone,” he said.