Deputy chief Andy Bowen of the New Mexico State University Police says the woman in her 50s was watching Saturday night's game when she felt what she thought was a bug bite. Then she realized she had been shot.
The shooting happened at about 8 p.m. at the stadium in Las Cruces.
Bowen says no one in the stadium heard a shot. The trajectory of the bullet was consistent with it being fired into the air outside the stadium and then coming down.
The woman was flown to a hospital in El Paso, Texas, where she was doing well Sunday morning.