Both planes were cleared later in the evening.
The threat was made while Flight 1184 was en route to Phoenix from Orange County, Southwest spokeswoman Ashley Dillon said. The plane was taken to an isolation pad after it landed in Phoenix.
The FBI's Joint Terrorism Task force worked with the Phoenix Police Department to screen the plane at Sky Harbor, FBI spokesman Manuel Johnson said.
The threat prompted Southwest to cancel another flight -- Flight 811 -- which had been scheduled to travel from Orange County to Phoenix, Dillon said. The flight was canceled before passengers boarded in Orange County, she said.
Local authorities screened and cleared the plane at John Wayne Airport.
Dillon said the threat wasn't specific to either flight, but Southwest decided to screen the two planes. Both planes will remain where they are for the night.
Dillon said she could not say who received the threat or exactly what the threat entailed.