Speaking at a news conference after a meeting of the International Monetary Fund (IMF) and World Bank's joint Development Committee in Washington, Carstens also said there would be no "structural" but only "transitory" damage to the economy.
The epidemic, which has claimed at least 22 lives and may have been responsible for 64 more, threatens to deepen Mexico's economic decline amid slumping US demand for Mexican exports.
The Mexican economy shrank 1.6 per cent in the fourth quarter of last year and may have contracted another 4.2 per cent in the first three months of this year, according to a central bank survey of 32 economists published in early April.
While no foreign government has banned travel to Mexico, several countries such as South Korea and Hong Kong have already advised citizens not to go there.
That could hurt a tourism sector that brought in $13.3bn in 2008 as Mexico's third-largest source of foreign currency behind oil exports and remittances from Mexicans abroad.
The World Bank said on Sunday that it was giving Mexico an immediate loan of $25m to help with medicine and medical equipment, and added that it would provide a further $180m to help the country set up operations to deal with the outbreak.