The vote will elect 2,600 judges and magistrates, including all Supreme Court justices.
It is part of a reform pushed by former President Andres Manuel Lopez Obrador and his protege and successor President Claudia Sheinbaum.
Lopez Obrador and Sheinbaum say the election will root out corruption in a flawed judiciary dominated by an out-of-touch elite and instead allow people to decide who should be a judge.
Opponents say the overhaul risks removing checks and balances on the ruling Morena party, by appointing judges friendly to their cause, and also allowing organised crime groups greater influence over the judicial system by running their own candidates. (Reuters)