The only goal of the game was scored by Mexico winger Hirving Lozano in the 35th minute. Following the match, Lozano was named the best player of the game.
"I don't know if it's the biggest victory in (Mexico's) history, but one of the biggest for sure," Lozano said. "It's great to start on the right foot when you are playing the world champions."
According to Germany's team, FC Cologne and the team's defender Jonas Hector missed his team's first 2018 FIFA World Cup match against Mexico due to a cold.
Besides Germany, France in 2002 and Spain in 2014 were the other defending champions to lose their opening matches and neither of the two teams advanced from the group stage.
According to FIFA, 78,011 fans attended the game, making it the second consecutive full house at the stadium so far at the tournament. Germany will next face Sweden, while Mexico will take on South Korea, with both games taking place on Saturday.
Earlier in the day, Serbia beat Costa Rica 1-0 in the teams' opening match of the World Cup in Russia's Samara.
The 2018 FIFA World Cup kicked off on Thursday and will continue through July 15, with a total of 64 matches set to be played at 12 stadiums across 11 Russian cities.