On Wednesday afternoon, local time, Judge Edmundo Román Pinzón was leaving the courthouse parking lot when he was struck by at least four bullets.
He served as president of the highest court in the state of Guerrero, which is where Acapulco is located, and was a senior judge.
The murder occurs as a number of deadly attacks on officials in the violent southern state are on the rise.
Despite interviewing witnesses and collecting CCTV evidence from the murder scene, police have not yet made any arrests in relation to the case.
In an effort to apprehend individuals involved, the security forces have also increased their activity in the resort town.
El Sol de Acapulco, the local newspaper, claims that the judge had been in control.
