The Federal Judicial Council said the general, whose name was not released, ordered that the suspect be tortured for several hours to get information about a soldier's death in July 2008 in the northern state of Chihuahua.
The victim was taken to a military installation, where he was tied up and soaked in water in order to receive electric shocks, while other suspects were being interrogated.
The torture began in the early hours of July 28, 2008, and ended at 9 AM (local time) when the victim died, "very probably" of a heart attack resulting from the electric shocks, the council said.
The court that sentenced the general ordered the defence ministry to offer a public apology, accept responsibility and vow that such acts will not be repeated.
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The general and defence ministry were ordered to pay USD 14,500 to relatives of the victim.
Mexico's armed forces and police have faced a slew of torture accusations amid a decade-long drug war.
The country's top general and police official apologised this month after a video surfaced showing federal officers and soldiers torturing a woman.
In another case, experts from the Inter-American Commission on Human Rights alleged that authorities tortured at least 17 suspects in the investigation into the disappearance of 43 students in 2014.
The attorney general's office said later that it was investigating more than 30 torture allegations in connection with the case.