The journalist was part of team of four from the international magazine who were recording the interview when the shootout occurred, according to a statement from the Attorney General's office of Chihuahua state.
It said the journalist was taken to a local hospital for treatment and that the rest of the team were being protected by the Attorney General's office.
The statement said the address where the interview took place had previously been searched by authorities in connection with the killing of two members of a criminal group there.
It said Friday's incident was under investigation "to find those responsible." It did not name the journalists or the alleged drug dealer.
Representatives from National Geographic did not immediately reply to a request for comment.The northern border state of Chihuahua is among Mexico's most violent, ranking sixth among the country's 32 departments and entities for homicides in 2018, according to government data.