The armed group entered the family's home in Juchitan, Oaxaca state, at 2:30 am yesterday and killed Victor Sanchez, 40, the singer of the tropical band Sensacion Caribu, the police said in a statement.
His wife and 11-year-old son were gunned down.
It was the second slaughter of a family this week in Oaxaca, a state that has been relatively spared of the drug violence afflicting other regions of Mexico.
The state prosecutor's office issued a separate statement saying that shots had been fired at Sanchez's house a few months ago and that a note threatening him with death was left behind at the time.
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In the previous massacre on Monday, eight shark fishermen from the same family were killed in Puerto Escondido, a beach resort famous among surfers.
Authorities said they were investigating whether the fishermen were involved in illegal activities at sea.
Officials did not specify what type of activities, but drugs are shipped along Mexico's Pacific coast.
Elsewhere in Mexico yesterday, authorities found six bodies on a path in the eastern state of Veracruz.
The victims included a police officer who had been missing since Saturday, three other men and two women, authorities said.
Tamayo is the 19th journalist killed since 2010 in Veracruz.