Both shared the meal at the restaurant named Quintonil, tweeted External Affairs ministry spokesperson Vikas Swarup.
Prime Minister Modi arrived here from the US on the fifth and final leg of his five-nation tour late Wednesday.
Modi on arrival to Mexico was received by the Mexican Foreign Minister Claudia Ruiz Massieu.
This is the first prime ministerial visit from India to Mexico after then Prime Minister Manmohan Singh's visit in 2012 for the G20 Summit.
Modi will hold bilateral talks with Mexican President Enrique Pena Nieto during which the issue of India's membership in the Nuclear Suppliers Group (NSG) is expected to come up.
Bilateral investments will be a major focus during the talks in Mexico.
. @p1yush_K The restaurant is called Quintonil— Vikas Swarup (@MEAIndia) June 9, 2016