Nashville police said week-old Yair Anthony Carillo was found at a home in Ardmore near the Tennessee line.
Tennessee Bureau of Investigation Director Mark Gwyn identified the arrested woman as Tammy Renee Silas, 39, of Ardmore. He said charges are "pending," but she was not immediately charged. She was being questioned and will be held at the jail in Morgan County, Ala., police said.
The infant underwent a medical checkup in Alabama and was in good health, authorities said. They were still making arrangements early Saturday to reunite him with his mother, 30-year-old Maria Gurrolla.
"This baby is a week old, and this child has spent half his life away from his family. I think it's time we reunite them," said My Harrison, a special agent with the FBI in Tennessee.
Authorities said they would be reunited through the Tennessee Department of Children's Services.
The baby and Silas were found about 10 p.m. CDT in Ardmore, about 80 miles south of Nashville, and Silas did not resist arrest, Gwyn said. Authorities said they had no word on a possible motive. Police in Nashville did not know if Silas has a lawyer.
The infant was taken from his home Tuesday, just four days after he was born. His mother told police a heavyset white woman with blonde hair arrived at her home posing as an immigration agent and attacked her with a knife.
At a Wednesday news conference, Gurrolla told reporters she had never seen the woman, who threatened to arrest her, then got a knife from the home and stabbed her several times.
"I need my baby back," the 30-year-old mother said Wednesday through an interpreter outside Vanderbilt University Medical Center.
Gurrolla said she did not see the woman take the baby because she ran to a neighbor's home. The neighbor, Eric Peterson, told The Associated Press that Gurrolla was "covered from her head to her toe with blood" with gashes on her neck and upper chest.
Gurrolla asked him to save her children from the "lady in the kitchen" who had a butcher knife. When Peterson got there, he saw a woman speeding away from the home. He brought Gurrolla's 3-year-old daughter back safely to his house, but found no baby, he said.
A task force of local, state and federal investigators got a break when they developed strong information on a car seen following the mother and baby from the parking lot of a Walmart store, police said.
Investigators on Friday had released a sketch of a suspect developed with Gurrolla's help and said it would be posted on billboards in Tennessee and other Southeastern states. TBI spokeswoman Kristin Helm said the billboard was intended to spur more tips from the public as leads in the case began to diminish.
Cathy Nahirny, a senior analyst for infant abduction cases at the National Center for Missing & Exploited Children, said there have been at least two other recent cases where an abductor used a ploy similar to the one used in this case.
"We need to get the word out to our immigrant communities," Nahirny said. "Anybody that claims they are from federal law enforcement agencies, you have the right and you should ask for photo identification."
Abductions of infants by strangers are rare, with only nine reported cases so far this year and five last year, according to the missing child center.
Nahirny said immigrant families have been targets of child abductions because of the assumption they will not tell police.
Gurrolla is Latina but her immigration status isn't clear. She was released from the hospital Thursday.
Harrison expressed relief that little Yair Anthony Carillo was found safe.
"Federal, state and local law enforcement have worked tirelessly for the last three days," she said. "It is not always that we have this outcome and we should be thankful."