The incident occurred less than an hour before United Airlines flight 1175 from San Francisco was set to land in Honolulu yesterday. The Boeing 777 plane was flying over the Pacific Ocean, the airline said.
There were 363 passengers and 10 crew members aboard the plane, CNN affiliate KHNL reported.
The plane landed safely as emergency responders and fire engines waited close to the runway.
Passenger Erik Haddad recorded video of the engine without its cover as the plane flew over the Pacific.
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"That looks bad, plane and simple," he wrote on Twitter describing the sight of pieces of metal missing from the front of the engine cowling.
Another passenger, Jeff Carter, posted a video showing the shaking in the cabin as the plane descended to land.
He heard a "big metallic bang," he said, and then the plane began to shake.
United Airlines spokesman Charles Hobart said the pilots safely landed the aircraft at Daniel K. Inouye International Airport, taxied to the gate, and the passengers got off the plane as they normally would.
"Pratt & Whitney is supporting the authorities in their investigation," the report quoted the company as saying said in a statement.