The girl gave birth less than two weeks ago by caesarian section at Madison Memorial Hospital in Rexburg, Fremont County Sheriff Ralph C. Davis and other authorities said.
"I wouldn't have believed a 10-year-old could conceive in the first place," Davis said.
A hospital spokeswoman would not discuss the condition of the girl or the baby and would not say whether either was still in the hospital Wednesday.
The story was first reported by KIDK-TV.
St. Anthony police began investigating on April 28 after medical personnel alerted police that a pregnant child had come in for treatment.
Guadalupe Gutierrez-Juarez, 37, of St. Anthony, was arrested the same day, Police Chief James Smith said.
"We had good information from witnesses," Smith said.
In documents that were filed April 29 in 7th District Court and obtained by The Associated Press, Gutierrez-Juarez is charged with one count of rape. He remained in jail with bail set at $250,000 pending a preliminary hearing May 13.
Authorities said Gutierrez-Juarez did not have legal documentation to live in the United States. His home town and nationality were not immediately clear, but police said they had received no complaints about him before investigating the pregnancy.
The investigation was continuing. Smith would not give details on the condition of the girl but said additional counts of rape could be filed.
"The prosecutor is still considering doing that," he said.
Prosecutor Karl H. Lewies did not return telephone calls Wednesday from The AP.
It's unclear who would take custody of the newborn or what will happen to the 10-year-old mother.
Child protection laws prohibit the Idaho Department of Health and Welfare from confirming whether the agency was contacted about the case, spokesman Tom Shanahan said.
"In a situation like that, we probably would be contacted by the hospital," Shanahan said. "If there was a crime committed we would be working with local law enforcement."
If the girl's home is found to be unsafe, a custody hearing would be held immediately and the courts would decide where to place her, Shanahan said.
"If they decide the child needs foster care, we would do that immediately," he said.
While a 10-year-old giving birth is highly unusual, it is not impossible, said Laurie Krieger, a medical anthropologist in Washington D.C.
"We do know that girls in the U.S. are menstruating sooner," a development which can speed up the production of sex hormones and make pregnancy possible earlier than might have been thought likely, Kreiger said.
Nutrition, body mass and other factors, including the fact that children in the United States weigh more than in past generations, contribute to early menstruation, she added.