A police chief and a councilor were killed by a gunman early on Thursday in Santa Catarina, a small town in the northern Mexico state of Nuevo Leon, the police told local media.
The gunman killed police chief Baltazar Gomez and local councilman Osvaldo Rodriguez inside a convenience store as they were returning from a funeral, said the police.
The attacker also hurt Councilwoman Socorro Escamilla. Another councilor Karina Dolores Garza escaped unhurt.
Gomez is the sixth law enforcement officer killed this year in Nuevo Leon which borders the United States' Texas. He took his post just six weeks ago, and local reports said he had received death threats from drug smugglers.
The region has seen a wave of violence as drug cartels battle for more lucrative routes into the United States.