"I can officially confirm that seven people have died of swine flu in Mexico," Jose Angel Cordova said late on Tuesday.
He added that there had only been 26 confirmed cases of people being infected with the virus in the country.
The minister also noted that all deaths from acute pneumonia were being treated as possible swine flu. His comments came as reports said that up to 159 people in the country had died of "suspected" swine flu.
Sixty-four cases of human swine flu infection have been confirmed in the United States and 13 in Canada, although there have been no fatalities. The United States has declared a public health emergency.
In Europe, swine flu cases have been confirmed in Spain and the U.K. Suspected infections have been reported in New Zealand, Israel, Brazil and Australia.
Countries around the world have begun measures to prevent a swine flu pandemic.
The World Health Organization has raised the level of swine flu pandemic alert from phase 3 to 4, implying a significant risk increase, two steps short of a full pandemic.
The consular section of Russia's embassy in Mexico has suspended its work until May 4 due to the swine flu outbreak.
All restaurants and cafes were shut down in Mexico City on Tuesday until May 6 over swine flu fears, with daily losses estimated at $10 million, the National Restaurant Association said.