Named Coatlicue, after a goddess in Aztec mythology representing the source of power and life, the computer will have a processing capacity of 314 petaflops.
"We want it to be a public supercomputer, a supercomputer for the people," President Claudia Sheinbaum told reporters.
A global race is underway to build ever-faster supercomputers to work in conjunction with AI systems.
The United States currently leads the field but Europe and Japan also have models in the top 10, according to an industry ranking of high-performance computing.
A petaflop equals 1,000 trillion calculations per second, a number expressed as 10 to the power of 15.
Pegaso, a privately-owned Brazilian computer, is currently rated the most powerful in Latin America with 42 petaflops.
Construction of Coatlicue will begin in January and last 24 months for a total cost of six billion pesos ($326.6 million), Jose Merino, director of Mexico's Digital Transformation Agency, said.
He added that the main uses of the supercomputer will be solving public issues requiring high computing capacity, such as climate prediction, crop planting and harvesting planning, and water, oil, and energy projects.
It will also be used in scientific research and support for entrepreneurial projects, among other purposes, he added.
Mexico's model will be no match for the world's most powerful computers, dubbed exascale computers, led by El Capitan.
Operated by the Lawrence Livermore National Laboratory in the United States, El Capitan has a processing capacity of 1.809 exaflops or quintillions (10 to the power of 18) of calculations per second.
Europe recently unveiled a rival, Jupiter, housed in western Germany, also able to perform at least one quintillion calculations per second, which is equivalent to about a million smartphones.
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