Veracruz Gov. Javier Duarte has ordered an exhaustive investigation into Martinez's death, he said in a statement.
Police found her body after receiving a tip from a neighbor that her house had been left open since early in the day.
In addition to Martinez, at least two other journalists have been found dead in Veracruz in a year, and none of the cases has been resolved.
In July 2011, a reporter on police matters with the newspaper Notiver, Yolando Ordaz de la Cruz, was found with her throat cut. A month earlier, gunmen killed Miguel Angel Lopez Velasco, a columnist and deputy editor with Notiver, as well as his wife and one of his children.
Media watchdogs consider Mexico one of the most dangerous countries in which to be a journalist.
There is disagreement on the number of journalist killings. Mexico's human rights commission says 74 were slain from 2000 to 2011. The New York-based Committee to Protect Journalists says 51 were killed in that time.