Relatives said the incident occurred yesterday as Barrientos rode in the back of his car with two bodyguards, in the southwestern town of San Francisco Zapotitlan, according to local media.
"I confirm that he arrived (at the hospital) with a shot to the temple, but later died of the wound," fellow Justice Hector Manfredo Maldonado told the state-run Guatemalan News Agency, known as AGN.
In 2012, the Supreme Court's criminal chamber, led by Barrientos, revoked 53 death-penalty sentences on the ground that they violated prisoners' "due process" and replaced them with 50-year prison sentences, the maximum allowed in the country.
Human rights activists also expressed their regrets.
Police and prosecutors are investigating the death.