Deputies detained the person during a traffic stop south of Tucson, Arizona, on Tuesday, the Pima County Sheriff's Department says.
The department did not immediately provide additional details.
It was not clear if the person being questioned is the person captured on surveillance video outside Nancy Guthrie's house that was released earlier on Tuesday.
The sheriff's department, along with the FBI's Evidence Response Team, was also conducting a search in Rio Rico, south of Tucson, on Tuesday night as part of the investigation.
It was expected to take several hours.
The news came hours after the FBI released surveillance images of a masked person with a handgun holster outside the front door the night the Nancy Guthrie vanished.
The person wearing a backpack and a ski mask can be seen in one of the videos tilting their head down and away from a doorbell camera while nearing an archway at the home of the 84-year-old mother.
The footage shows the person holding a torch in their mouth and trying to cover the camera with a gloved hand and part of a plant ripped from Nancy Guthrie's yard.
The videos gave investigators and the public their first glimpse of who was outside Nancy Guthrie's home just outside Tucson, but the images did not show what happened to her or help determine whether she is still alive.
FBI Director Kash Patel said the "armed individual" appeared to "have tampered with the camera".
The videos were pulled from data on "back-end systems" after investigators spent days trying to find lost, corrupted or inaccessible images, Patel said.
Investigators have said for more than a week that they believe Nancy Guthrie was taken against her will.
She was last seen at home January 31 and reported missing the next day.
DNA tests showed blood on her porch was hers, authorities said.
She has high blood pressure and issues with mobility and her heart, and she needs daily medication, officials have said.
Until now, authorities have released few details, leaving it unclear if ransom notes demanding money with deadlines already passed were authentic, and whether the Guthrie family has had contact with whoever took Nancy Guthrie.
Savannah Guthrie posted the new surveillance images on social media on Tuesday, saying the family believes Nancy Guthrie is still alive.
Investigators had hoped cameras would turn up evidence right away about how Nancy Guthrie disappeared from her home in an secluded neighbourhood.
But the doorbell camera was disconnected early on February 1.
While software recorded movement at the home minutes later, Nancy Guthrie did not have an active subscription, so Pima County Sheriff Chris Nanos had initially said no footage could be recovered.
Officials continued working to get the video.
Heartbreaking messages by Savannah Guthrie and her family shifted from hopeful to bleak as they made pleas for whoever took Nancy Guthrie.
In a video just before a purported ransom deadline on Monday, Savannah Guthrie appeared alone and spoke directly to the public.
"We are at an hour of desperation," she said. "We need your help."
Much of the nation is closely following the case involving the longtime anchor of NBC's morning show.
Connor Hagan, a spokesperson for the FBI, said the agency was not aware of ongoing communication between Guthrie's family and any suspected kidnappers.
Authorities also had not identified any suspects, he said.
