Police said the search for Sjodin is continuing. Police said no other information will be released until a news briefing Tuesday morning.
Authorities say Alfonso Rodriguez Jr., 50, was arrested in Crookston, Minn., where he lives, and is being held in the Tri-County Correctional Center.
Dru Sjodin, of Pequot Lakes, Minn., has been missing since Nov. 22, when she left her job at the Columbia Mall in Grand Forks, about 30 miles from Crookston. Her 1994 red two-door Oldsmobile Cutlass was found in the mall parking lot.
Soon after Sjodin disappeared, her boyfriend, Chris Lang, called the student's roommate, saying he had received two calls. The first was cut off and Lang heard Sjodin say, "Oh, my God," before the phone went dead. A second call a couple of hours later was only static and the sound of numbers being pressed.
The case had drawn more than 1,300 volunteers who have searched the area without success. In addition, about 30 FBI agents, along with investigators from 20 different agencies in three states and the Canadian province of Manitoba, were working on the case. A $140,000 reward has been offered.
Earlier Monday, about 150 volunteers again waded through waist-deep snowdrifts and crossed frozen ravines on farmland in the search for Sjodin.
Law enforcement agencies also have conducted smaller searches based on a few of the nearly 900 leads authorities have received in the disappearance of Sjodin, Grand Forks police Sgt. Michael Hedlund said.
"Twenty different law enforcement agencies have been working hard and long on the investigation," said Sjodin's mother, Linda Walker, in a CBS News Early Show interview.
"I can't even begin to thank all of the people," said Walker. "I know there have been a lot of Dru's classmates that chose to be the entire time up there and not spend the holidays with their own families."
"We're gonna find you Dru, keep hanging on," said Sjodin's brother, Sven, at a news conference on Sunday. "We're just around the corner from you and we know we're gonna find you."
Divers from as far as New York and Los Angeles searched the area's rivers and streams, and the U.S. Border Patrol searched by air.
Sjodin, 22, of Pequot Lakes, Minn., was last seen Nov. 22 after leaving work at the Columbia Mall in Grand Forks. Authorities believe she may have been abducted while she was talking to her boyfriend on her cell phone.
She is described as 5'5" tall, 130 pounds, with blue eyes and frosted blonde hair. She was last seen wearing a pink and purple V-neck blouse, black pants, black blazer, black loafers and a black pea coat, carrying a small black purse.
Sjodin's disappearance has set nerves on edge in the Dakotas and Minnesota.
In Grand Forks, retailers said supplies of stun guns and pepper spray are selling fast.
"I'm sure there's a lot of scared young women right now," said Greg Washburn, manager of the camping supplies department at Cabela's.
Sjodin's family has set up a Web site www.finddru.com to appeal for volunteers, distribute posters and buttons, and otherwise get out the word on the search.
Anyone with information on Sjodin's whereabouts is asked to call police in Grand Forks at 701-787-8000, call the tips line at 701-780-8213, or e-mail: firstname.lastname@example.org.
"Dru is an extremely outgoing young lady," said her mother. "She has a gift of being able to communicate with anybody. She would make anybody feel comfortable being around her. Outgoing. A beautiful smile ... Just warms the room as she walks in."