Spc. Kirsten Fike was two hours into the training mission near Yuma when she collapsed Wednesday. She died the next day at a hospital, guard spokesman Capt. Cory Angell said.
Angell said the guard has not yet determined the cause of death.
Fike, 36, joined the guard in June after having served on active duty in the Air Force. She was a member of the Greensburg-based detachment of the 28th Military Police Co. About 60 members of the company were serving their annual two-week training by working along the border.
All incoming National Guard soldiers are advised about the heat precautions before and after arriving in Arizona, said Maj. Paul Aguirre, spokesman for the Arizona National Guard.
Fike is survived by her 13-year-old son, Cody, Gov. Ed Rendell said in a statement.
President Bush announced plans in May to send 6,000 National Guard troops from across the country to support the Border Patrol. Bush said the mission would free up Border Patrol officers for active patrols while the guard members built fences, conducted routine surveillance and took care of administrative duties.