The fire, smoldering 11 miles south of Arivaca, has burned 350 acres and is 40 percent contained, officials said.
The fire, with a cause still under investigation, started Sunday morning and is burning mainly grass in lowland drainage areas, said Buzz Ostermann, a spokesman for the U.S. Forest Service.
The blaze originated south of the border and burned about 500 acres in Mexico, which is not included in the U.S. acreage total, Ostermann said.
"Thankfully the winds have died back," Ostermann said. Containment is expected in a couple of days, he said.