The country's 1.4 million health workers will be the first to get the shots, followed by the elderly, those with underlying health conditions that make them more vulnerable to the disease, and teachers.
Foreign Relations Secretary Marcelo Ebrard said Mexico was the first country in Latin America to get the vaccine, though others were close behind.
In Costa Rica, which is the third country in the region to begin using the Pfizer vaccine, the first shot was given Thursday to Elizabeth Castillo, 91.
Argentina, which has run into problems obtaining the Pfizer vaccine, received a flight carrying 300,000 doses of the Russian Sputnik V vaccine.
Argentina plans to become the first country in Latin America to administer the Russian vaccine starting next week.