Maxon was arrested in 2006 and admitted drowning her son, Alexander. Psychologists who examined her said Maxon believed her son was possessed by the devil and would destroy the world unless she put him in water.
Defense attorney Joetta Keene called Maxon "a gentle soul whose mental illness took over."
Prosecutor Alana Minton said justice was served by the outcome of the case.
During the trial, a Texas Ranger, two psychologists and Maxon's sister testified about her failing mental state.
Maxon was living in the former Soviet republic of Moldova when she met her husband, Michael, through a dating service.
Alexander was born in June 2005. Nine months later the Maxons learned he was developmentally delayed, and his mother's mental health soon began deteriorating, according to one of the psychologists who testified during the trial.
Maxon drowned her son while her husband was out grocery shopping.
Michael Maxon, 54, was arrested this week on a charge of abandoning a child. His attorney, Jack V. Strickland, said Maxon may have used poor judgment by leaving his son home alone with his mentally unstable wife but didn't break any laws.