Authorities identified him as Tom Begaye, 27, but did not offer details as to a possible connection to the children. Begaye is scheduled to appear in U.S. Magistrate court Wednesday.
CNN's attempts to reach Begaye were not immediately successful, and CNN could not determine if he has an attorney.
Both the girl, identified as Ashlynne Mike, and her brother, Ian, were kidnapped Monday afternoon near their home in Fruitland, authorities say.
Ashlynne's body was found early Tuesday more than 20 miles away near Shiprock Monument, the FBI tells CNN.
Both children are members of the Navajo nation.
The children's parents filed missing persons reports with police early Monday evening, the Navajo Nation said. Later that evening, a motorist picked up Ian Mike, 9, who was walking along Navajo Route 13.
"Ian Mike told Shiprock Police that the driver who abducted the two children had taken them toward the Shiprock pinnacle where he came upon a dead end road and let the boy out. The abductor returned without Ashlynne Mike and told the young boy to go home," a Navajo Nation press release said.
Ojo Amarillo Elementary, where Ashlynne attended, released a statement expressing "great sadness," and asking parents to help increase security.
"Our hearts are broken. Our students are family ... I also ask our parents and staff to tell their children how much they love them," Superintendent Dr. Colleen Bowman said.
"In light of this incident, we are asking our parents to be with their children when their school bus picks up and drops them off to help ensure their safety."
New Mexico Gov. Susana Martinez called the killing a "horrible, horrible tradgedy," CNN affiliate KOAT
A multiagency task force, including the FBI, the Navajo Nation Division of Public Safety, New Mexico State Police, San Juan County Sheriff's Office, Farmington Police Department and the U.S. Marshals Service, participated in the investigation.