The damaged engine can be seen in video a passenger tweeted from United Airlines Flight 1175.
The flight took off from San Francisco International Airport just after 12 p.m. ET and landed at Honolulu's Daniel K. Inouye International Airport at 5:42 p.m. ET.
The aircraft involved is a Boeing 777. It has two engines and is designed to fly on just one engine for more than three hours over water.
Here are more tweets from that passenger:
An engine cover came off during its flight from California, the airline said.
"Our pilots followed all necessary protocols to safely land the aircraft," United said in a statement, adding that all passengers departed the Boeing 777 normally at the gate.
The airliner landed as emergency responders waited nearby, said Hawaii Department of Transportation spokesman Tim Sakahara.
An emergency was declared due to a vibration in the right engine, said Federal Aviation Administration spokesman Ian Gregor said in an email.
The FAA will investigate.
(The Associated Press contributed to this report.)
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