The men took away Salvador Adame, owner of a local television channel, in the western town of Nueva Italia, a family member said.
The town lies in Michoacan state, one of the regions worst hit by recent years of drug gang-related violence.
Armed and hooded men "took him away from a shop" late on Thursday evening, said the family member, who asked not to be named.
President Enrique Pena Nieto on Wednesday promised to boost protection for journalists and tackle impunity for those who attack them.
Media rights groups say five reporters have been murdered in Mexico in 2017 and more than 100 have been killed since 2000.
The latest was Javier Valdez, 50, a renowned reporter and AFP contributor who wrote about drug gangs in north-western Sinaloa state.