The ministry said in a statement yesterday that the child was premature and died at birth. It was born to a 25-year-old woman from the southern state of Oaxaca on November 5 last year.
The ministry says it took several months to confirm the microcephaly, which is characterised by newborns with abnormally small heads, was related to Zika.
From November 2015 through the end of January, there have been 7,634 confirmed cases of Zika in Mexico, including 4,252 in pregnant women.
Zika is a mosquito-borne virus that has spread through Latin America and the Caribbean since 2015.