The FBI identified him as 21-year-old Eslam Ibrahim Mohamed El-Dessouki. He was taken into custody on an administrative immigration violation as an out-of-status student. The arrest occurred without incident, the FBI said in a statement.
Officials continue to say that there is no reason to believe that El-Dessouki or the other missing students are connected to any terrorist or criminal enterprise.
The students arrived in the United States last month and were being sought by authorities after failing to turn up for an exchange program at Montana State University.
The Egyptian men were among a group of 17 students who arrived at John F. Kennedy International Airport in New York from Cairo on July 29 with valid visas, according to U.S. authorities and university officials.
The other six have arrived at the Bozeman, Mont., campus for a month-long program on English language instruction and U.S. history and culture, university spokeswoman Cathy Conover said. When the 11 didn't turn up by the end of the last week, the FBI issued a lookout to state and local law enforcement, said FBI Special Agent Richard Kolko.
"At this point all they have done is not show up for a scheduled academic program," Kolko said. "There is no threat associated with these men."
The 11 are between 18 and 22 years old, said a law enforcement official who spoke on condition of anonymity because the search for the men is continuing.
U.S. Immigration and Custom Enforcement declined to make their names public.
The government probably will seek to send the students home once they are located because they have violated the terms of their visas, the official said.
The government tightened the student visa process after the Sept. 11, 2001, terrorist attacks when it learned that four of the hijackers entered the country on foreign student visas.
The school has tried repeatedly to contact the students, Conover said, including sending e-mails. When that failed, the school notified Homeland Security officials and registered the Egyptians as "no-shows" in the system developed after Sept. 11 to track foreign students, Conover said.
They were participating in an exchange program Montana State arranged with Mansoura University in Mansoura, Egypt.
"We hope this doesn't cast doubt on this program because we think it's important to have international students on our campus and in our community," Conover said.