The man, identified as Anil Tuvanc Uskanli -- a Turkish national born in 1991-- was subdued by crew members and passengers, including an off-duty Los Angeles police officer.
He is expected to face federal charges for interference with a flight crew, FBI special agent Paul Delacourt told reporters.
Investigators are still trying to determine the motive behind the disturbance.
Allison Forburger, who lives in Hawaii, where she works for the Navy, said the man was moving toward the first-class section of the cabin with a blanket over his head when a flight attendant directed him to stop.
As the suspect approached the drink cart at the rear of first class, the flight attendant in economy told him, "Sir, please stop. Sir, I need you to go back to your seat."
Forburger, sitting in an aisle seat at the front of economy class, said other passengers helped the flight attendant get the passenger back toward the back of the plane.
The man did not fight with the other passengers and left a black laptop he had been clutching to his chest on the drink cart, she said.
The incidents is still under investigation but officials said there were not other threats to the American Airlines or any other aircraft. No explosives were found on the airplane and the cockpit was not breached, Delacourt said.
'Taped him to his chair'
Passenger Lee Lorenzen told CNN affiliate KITV that the flight attendant told the man: "You're not coming in here" and used the cart to block his path.
But Forburger said the cart was already in the way as the flight attendants were picking up dishes from first-class passengers who had just finished lunch.
She recalled the crew member saying, "I need help, I need help, I need to get this guy back to his seat."
She lost sight of the suspect, but Lorenzen told KITV and CNN affiliate KGMB/KHNL the man was duct-taped to a seat.
"It took seconds," Lee Lorenzen told KGMB/KHNL. "He was pushing against the cart and a bunch of guys grabbed him. They found some duct tape. There were pillows and blankets. And they taped him to his chair."
One of the passengers who helped was an off-duty law enforcement officer, the FBI said.
The suspect was met by authorities when the Airbus 321 landed in Honolulu.
"Due to a disturbance during the flight, the crew requested that law enforcement meet the aircraft upon landing in Honolulu," American Airlines said in a statement.
Video from KGMB/KHNL showed two law enforcement officers escorting a person with hands behind their back off the plane.
Incident at LAX
The Department of Homeland Security tweeted that the person was detained and the incident appeared to be isolated.
"At this time, there are no other reports of disruptions to flights," the department tweeted. We continue to monitor all flights out of an abundance of caution and will provide updates as necessary."
President Donald Trump was also briefed on incident, Trump's spokesman Sean Spicer said.
Earlier, the man, who purchased his ticket around midnight, had an encounter with airport personnel at the airport in Los Angeles, an official briefed on the incident told CNN. The man attempted to use a door off-limits to the public after 3 a.m. PT (6 a.m. ET) while waiting for his flight.
The suspect was cleared to fly after that incident.
The airliner left Los Angeles International Airport at 8:43 a.m. PT (11:43 ET) for the nearly six-hour flight, according to FlightAware.com.
Two F-22 Raptors from the Hawaiian Air National Guard escorted the plane for the final part of the flight, Navy Cmdr. Dave Benham said.