The scare comes after a similar incident on Monday
The Delta Airlines flight was diverted after the pilot reported a disturbance in the cabin.
Edward A Stephenson, 36, of Venice, California, was arrested and charged with interfering with a flight crew member and attendants, FBI spokeswoman Sheila Thorne said.
Delta Flight 357 landed safely in Shreveport, Louisiana, at around 1500 local time (2000 GMT).
It was escorted by US F-16 fighter jets.
The plane continued on to Los Angeles where it landed without incident.
Four of the passengers were so shaken by the incident they got off the plane at Shreveport, according to reports.
'Strange note'
US Attorney Bill Flanagan said the note was in response to an announcement by the pilot that they would be taking a different flight path.
"The passenger handed a note to the flight attendant that contained language that the pilot should not divert from the original flight path, and some other language which seemed bizarre," Mr Flanagan said.
"It didn't make a lot of sense, but at the same time it was alarming".
The man did not make any physical threats, Mr Flanagan said.
According to police, Mr Stephenson appeared disoriented when he was taken off the plane.
FBI spokeswoman Shelia Thorne said prosecutors planned to seek a mental evaluation.
Passengers getting off the plane at Los Angeles International Airport said Mr Stephenson stayed in his seat until the plane landed in Shreveport and an FBI agent came aboard and took him into custody.
Several said they were unaware anything had occurred until they saw two military jets pull alongside their plane.
Earlier incident
On Monday an American Airlines plane travelling from Los Angeles was forced to make an escorted landing in Chicago after a man burst into the cockpit.
Passengers and pilots subdued the man and the plane, with 162 people on board, landed safely.
Edward Coburn, 31, has been charged with interfering with a flight crew.