The plane, traveling from Addis Ababa to Rome with 202 passengers and crew members, landed safely in Geneva with no report of injuries, the New York Times said.
"Everybody was safe from beginning to end -- no problem," Swiss police spokesman Eric Grandjean said.
Voice of America identified the pilot as Hailemedhin Abera Tegegn, 31. Ethiopian government spokesman Redwan Hussein said there was no apparent reason Tegegn would need to seek asylum. He has no criminal record and no history of mental illness, Hussein said.
"As it is an Ethiopian Airlines pilot, he has several opportunities to apply for any airlines, withhold his dignity, and also he has a host of visas. ... So he does not have to hijack his own plane and [get] himself into hot water," he said.
Tegegn is in Swiss custody and faces up to 20 years in prison if convicted of hijacking the plane, Voice of America said.
Other officials said passengers didn't realize the Boeing 767-300 was being hijacking until it landed. When it did, they were made to exit the plane on the tarmac with hands over their heads. Travelers were searched for weapons before being escorted to the airport, the Wall Street Journal said.
The plane was in Italian airspace when the unidentified Ethiopian co-pilot took control after locking the cockpit door when the pilot left to use the bathroom, the Times said. Italian fighter jets accompanied the jetliner out of the country's airspace. French fighter jets then escorted it through that country's air space and into Switzerland.
After the plane landed, police spokesman Jean-Philippe Brandt said, the co-pilot crawled out of a cockpit window, climbed down a rope and surrendered to police.
"His act has been motivated by the fact that he feels threatened in his [country] and wants to make an asylum claim in Switzerland," Swiss police spokesman Philippe Grangean said.
Geneva International Airport was shut down during the incident but later reopened, CNN said.
A commercial jet liner being hijacked by a member of the crew is rare though not unheard of, the Wall Street Journal said.
In the last 63 years, 10 such incidents have been recorded. More than half were planes originating in Cuba in the 1960s.