Thirty-four people were infected locally, while three were infected abroad, Health Minister Mercedes Juan said on Wednesday.
Two-thirds of the cases were confirmed in the southern state of Chiapas. The rest of them were found in Oaxaca, Nuevo Leon, Tamaulipas, Jalisco, Sinaloa and Queretaro, Xinhua news agency reported.
More than half patients were women between the ages of 16 and 24.
Given that the virus can lead to birth defects in infected fetus, the ministry plans to provide the country's gynecologists with special training in pre-natal care, said Juan.
The ministry's director general of epidemiology, Cuitlahuac Ruiz Matus, warned that the number of cases in Mexico could spike starting in April or May, when temperatures rise and the rainy season begins. He urged to control the source of the virus, the Aedes aegypti mosquito.
Zika has been linked to birth defects and has symptoms including fever, muscle and joint pain, headache, nausea and rashes in adults.
The virus has spread rapidly through Latin America.