2015 AFRICA CUP - CAF - EBOLA AND NATIONS CUP - SOUTH AFRICA RULE OUT BEING 2015 HOSTS
The Confederation of African Football (CAF) approached South Africa last week, after Morocco asked to postpone the event because of the Ebola crisis.
"I can tell you unambiguously and categorically that hosting is a no no," Mbalula told South African media.
"Our budget cycle will not allow it - it is totally impossible."
South Africa were among seven countries sounded out by CAF as possible replacements for Morocco, who have major concerns about hosting the 17 January to 8 February tournament.
Almost 4,500 people have died in the Ebola epidemic that broke out in west Africa at the start of the year and Morocco youth and sports minister Mohamed Ouzzine said on Thursday he does not think the tournament can happen as planned.
Moroccan officials will meet with CAF on 3 November to discuss the situation.
Whatever the outcome, South Africa have made their stance clear.
Mbalula said the country had a responsibility to help fight to help fight the Ebola epidemic, with the United Nations predicting a surge in deaths and cases.
"We do not have a ready-made abundance of resources to be shifted to the Nations Cup, " he added.
"We would like to give this one a pass.
"We will share the responsibility to fight Ebola - we are not immune to that.
We must be prepared to share our skills, our doctors, to reinforce the research to find a vaccine."
South Africa have twice been emergency hosts of the competition, replacing cash-strapped Kenya in 1996 and strife-torn Libya last year.
Ghana are another of the countries to have been approached by CAF, according to the sports minister of the west African country.
The identities of the other five countries have not been officially revealed.
Most of the Ebola deaths have been in Guinea, Liberia and Sierra Leone.
CAF has barred Guinea and Sierra Leone from hosting Nations Cup qualifiers.
Liberia were eliminated in the preliminary rounds.
Guinea have staged home fixtures in Moroccan commercial capital Casablanca.
Sierra Leone, having failed to secure a neutral venue, had to play home games against the Democratic Republic of Congo and Cameroon in Lubumbashi and Yaounde respectively.