Navy spokesman Jose Luis Vergara says the four marines were assigned to duty as drivers and were kidnapped and killed on April 18 as they returned from a training course in the Gulf coast state of Veracruz.
Marines have largely taken over security duties in many parts of Veracruz because the Zetas intimidated or corrupted local police.
Vergara said Friday that suspect Marcos Jesus Hernandez Rodriguez was caught with guns and drugs on Wednesday.
He said another Zetas member detained earlier had implicated Hernandez Rodriguez in the crime.
Vergara described the suspect as a top Zetas hit man suspected in at least seven other killings.