The Boeing 767-300 plane with 202 passengers and crew aboard had taken off from the Ethiopian capital, Addis Ababa, and landed in the Swiss city at about 6 a.m. (0500 GMT). Officials said no one on the flight was injured.
Geneva airport chief executive Robert Deillon told reporters that the co-pilot, an Ethiopian man born in 1983, took control of the plane when the pilot ventured outside the cockpit.
"The pilot went to the toilet and he (the co-pilot) locked himself in the cockpit," Deillon said.
The man "wanted asylum in Switzerland," he said. "That's the motivation of the hijacking."
The hijacking began over Italy, Switzerland's southern neighbor, and two Italian fighter jets were scrambled to accompany the plane, according to Deillon.
Passengers on the plane were unaware it had been hijacked, officials said.
A few minutes after landing in Geneva, the co-pilot exited the cockpit using a rope, "then he went to the police forces who were on the ground close to the aircraft," Geneva police spokesman Eric Grandjean said. "He announced that he was himself the hijacker."
It was not immediately clear why the co-pilot, whose name wasn't released, wanted asylum.
Police escorted passengers one by one, their hands over their heads, from the taxied plane to waiting vehicles.
Geneva prosecutor Olivier Jornot said Swiss federal authorities were investigating the hijacking and would press charges that could carry a prison sentence of up to 20 years.
Geneva airport was initially closed to other flights, but operations resumed around two hours after the hijacked plane landed. "We hope everything will return to normal in the afternoon," Deillon said.
Ethiopian Airlines is owned by Ethiopia's government, which has faced persistent criticism over its rights record and alleged intolerance for political dissent.
Human Rights Watch says Ethiopia's human rights record "has sharply deteriorated" over the years. The rights group says authorities severely restrict basic rights of freedom of expression, association, and assembly.
The government has been accused of targeting journalists, opposition members, as well as the country's minority Muslim community.
There have been numerous hijackings by Ethiopians, mostly fleeing unrest in the East African nation or avoiding return.
An Ethiopian man smuggled a pistol onto a plane and hijacked the Lufthansa flight going from Frankfurt to Addis Ababa in 1993. He demanded it be flown to the U.S. because he was denied a visa.
In June and April 1994, the Ethiopian Airlines suffered two hijacking at the hands of passengers who demanded to be flown to locations in Europe, according to the Aviation Safety Network, which tracks aviation hijackings and other incidents.
In 1995, an Ethiopian man trying to avoid being sent back home used a knife from a food tray to commandeer an Olympic Airlines jet just before it landed in Athens, Greece. Police overpowered the hijacker with no injuries to any of the 114 people on board, according to AP reports. Also that year, five armed men seized an Ethiopian Airlines jetliner and demanded the plane be flown to Greece and then Sweden. It was instead diverted it to Al Obeid, about 300 miles (480 kilometers) west of Khartoum, Sudan.
In 1996 a flight from Ethiopia to Ivory Coast via Kenya was seized by hijackers who then demanded to be flown to Australia. That flight ran out fuel and crashed off the island nation of Comoros, killing 125 people, according to the Aviation Safety Network.
In 2001, five military pilot trainees who flunked flight school reportedly wrested control of a plane during a flight from the Bahr Dar, in northwestern Ethiopia, to the capital Addis Ababa and demanded to be flown to Saudi Arabia. The plane didn't have enough fuel so it landed in neighboring Sudan, according to AP reports.
In 2002 two passengers armed with small knives and an explosive device attempted to hijack a domestic flight but were shot and killed by in-flight security personnel, the Aviation Safety Network reported.