The woman, from the town of Pijijiapan, delivered the six pound (2.8 kilo) boy in a hospital in the city of Tuxtla Gutierrez yesterday.
After an evaluation, the hospital's pediatric center "confirmed that [the infant] is clinically healthy," the health ministry said in a statement.
The woman is one of six known to have contracted Zika while pregnant.
Zika, which is spread by mosquitos, has been linked to microcephaly -- a birth defect in which the infant is born with an abnormally small head. There is no cure for microcephaly and no vaccine against Zika.
Two of the women are beyond their 28th week of pregnancy, and several tests show no sign that they are carrying a fetus with microcephaly. The other three have still not reached the 28 week mark, the statement read.
Of the 80 registered Zika cases in Mexico, 45 are in the southern state of Chiapas, including three of the pregnant women.
On average Mexico, population 122 million, has 600 cases of microcephaly per year. That figure has not change since the Zika virus outbreak in Latin America, officials said.
