Laura Eimiller of the FBI's Los Angeles field office said the flight left Los Angeles International Airport at 2:12 p.m. before the threat was received by telephone. She didn't provide further details.
"The FBI and law enforcement partners are responding to conduct an investigation of the aircraft, as well as to determine the person or persons responsible for the threat," Eimiller said in a statement.
F-16s were scrambled out of Davis-Monthan Air Force Base in Tucson to monitor the flight as a precaution as it flew into Sky Harbor, according to NORAD officials.
Flight 2675 landed safely at Phoenix Sky Harbor International Airport at about 3 p.m., and authorities in Los Angeles asked Phoenix police to check out the possible threat.
The plane's crew and 143 passengers got off the plane and boarded several buses. All of the passengers were being interviewed by investigators, said Sgt. Steve Martos, a Phoenix police spokesman.
It's possible that "the people on the plane may know" something about the threat, Martos said.
A bomb squad and police dogs were going through the plane Monday evening, police said.
Sky Harbor spokeswoman Julie Rodriguez said the plane was isolated on the tarmac away from terminals.
Flights were taking off and landing only on the airport's two south runways Monday evening due to the investigation, and some arrivals were delayed, Rodriguez said.
Martos said it would probably take "a couple hours" for police bomb squad technicians and bomb-sniffing police dogs to go through the plane.
Authorities said a thorough search of the plane and the passenger interviews are common operating procedure when a threat is received.
A spokeswoman for Dallas-based Southwest Airlines Co. said the airline would accommodate passengers by booking them on other flights.