The soldier reportedly dumped the body of his wife, who was two months pregnant, in a landfill near the Mexican border city of Ciudad Juarez, authorities in Mexico announced on Wednesday.
According to the report, after calling El Paso police to report the murder, Nevares shot himself in the head as he sat in his car, leaving a letter.
The content of the letter or the cause of the argument between the couple has not been reported.
The body of the pregnant woman was found on Tuesday.
There have been many reports of American soldiers returning from US-led wars in Iraq and Afghanistan killing or attempting to kill themselves as well as family members and friends due to what American military authorities have referred to as Post-Combat Stress Syndrome.
A US soldiers has killed his pregnant wife following an argument on the national Thanksgiving Day holiday, and shot himself dead after confessing to police in a phone call.
The American soldier, Johnny Ray Nevares, strangled his 20-year-old wife, Cristal Nevares, to death at their residence in the border town of El Paso, Texas, after an argument last Thursday, during a major holiday that is widely known to bring families closer together, AFP reported Thursday.