Brian Quigley, a spokesman for the U.S. Consulate in Monterrey, said U.S. citizen Lizbeth Marin was shot Friday and later died of the wound. Quigley said he could provide no details on the shooting.
"We are in contact with the corresponding Mexican authorities who we hope will conduct a thorough and expeditious investigation," Quigley said.
The newspaper El Bravo reported that Marin was hit by a stray bullet at a friend's home in Matamoros, across the border from Brownsville, Texas.
The paper cited a witness as saying a Mexican army soldier accidentally fired the round that hit Marin.
Authorities in Tamaulipas state were not immediately available to comment, and the press office at Mexico's Defense Department said it had no immediate information on the report.
El Bravo reported that relatives and friends of the dead woman—who was reportedly living in Matamoros—gathered outside a funeral home Sunday with banners demanding punishment for her death, and asking soldiers to leave the city.
A photo published by the paper showed several people holding up a banner reading "We demand justice, Presidents of Mexico and the United States, in the death of the innocent woman Liz Marin at the hands of the army."
The newspaper El Universal cited a witness who said the shot appeared to have come from a soldier participating in a raid, whose gun went off as he climbed into a vehicle.
The Mexican government has dispatched thousands of army troops to combat drug cartels, and soldiers have sometimes been accused of abuse, including firing on civilians at highway checkpoints.
Drug-related violence has cost nearly 14,000 lives in Mexico since late 2006, when the government launched an anti-drug offensive.
Also Monday, prosecutors in Baja California state said police found the bruised body of a 54-year-old American woman at a house near the border city of Tijuana.
The state attorney general's office says the woman's body had signs of blunt injuries including contusions to the head, neck and face.
U.S. consular authorities say they do not have any immediate information on the woman's name, hometown or nationality.
Investigators said Monday they have not yet performed an autopsy or determined the cause of death. The body was found Sunday.