Cpl. Armando Torres III, a 25-year-old Iraq War veteran and member of the Marine Individual Ready Reserve, was taken by armed men from his father's ranch in La Barranca, Tamaulipas on May 14.
Torres had driven across the border at the International Port of Entry Bridge at Progresso, Texas.
His father, Armando Torres II, and uncle, Salvador Torres, both Mexican citizens, were also taken, the FBI said. The three men have not been heard from since.
The senior Torres is apparently involved in a land dispute, Tamaulipas state officials told CNN, and neighbors said the kidnapping could be related.
An official said the U.S. Consulate was working directly with Mexican authorities to try to free the three men.