Merkel, who is traveling with a delegation of German lawmakers and business executives, arrived on Sunday and was feted at the Los Pinos presidential palace with a state dinner.
The German leader's official agenda of meetings starts on Monday, when she and Calderon are scheduled to discuss issues that include investment, the environment, public safety and fighting poverty.
Merkel will also meet with members of the Mexican-German Chamber of Commerce and of Mexico's Congress before hosting a dinner for Calderon, ahead of her return flight to Germany late on Monday.
Germany is Mexico's fourth largest trade partner after the United States, China and Japan.
Mexico is Merkel's last stop in her tour of Latin America, which included visits to Brazil, Peru and Colombia.
In Columbia Merkel promised German support in dealing with the country's history of human rights violations, killings and expulsions due to decades of paramilitary violence.
Estimates are the 57,000 people were killed by paramilitary violence between 1964 and 2004 in Columbia, while between two million and four million were driven from their homes.