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.
"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 buses. All of the passengers were being interviewed by investigators, said a Phoenix police spokesman.
A bomb squad and police dogs were going through the plane Monday evening, police said.
An airport spokeswoman 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.
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.
The Associated Press contributed to this report.