Maricopa County sheriff's deputies arrested 33-year-old Tanya Nareau of Mesa on Tuesday after receiving a tip.
Deputies say they spoke with a family friend who had the child and confirmed Nareau gave the girl to him for gun.
Deputies say Nareau felt the friend would do a better job raising the child than she would.
Authorities say Nareau has been charged with the unlawful sale of a child and solicitation to possess a weapon by a prohibited person.
It was unclear if Nareau had legal representation.