The blast late Tuesday near a town in Michoacan state destroyed the armored vehicle in which the troops were traveling, according to the internal document.
Military planes and helicopters were deployed to help the casualties, it said.
President Claudia Sheinbaum described the deaths as "deplorable" and expressed solidarity with the victims.
Warring criminals in the region have a history of planting improvised landmines and attacking security forces with explosive-laden drones.
Several soldiers have been killed in similar explosions in the past.
Criminal violence, most of it linked to drug trafficking, has claimed around 480,000 lives in Mexico since 2006 and left more than 120,000 people missing.
US President Donald Trump has designated six Mexican drug trafficking groups terrorist organizations, fueling speculation that he might order military strikes against them.
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