Crittenton is accused of murder in the death of a mother in Atlanta.
Crittenton was about to get on a flight to Atlanta when he was apprehended by federal agents and police, said Laura Eimiller, a spokeswoman for the FBI Los Angeles field office.
Crittenton, 23, faces murder charges in Atlanta in connection with the shooting death of 22-year-old Julian Jones, Atlanta police have said.
Jones was killed during a drive-by shooting August 19.
Crittenton, who played for Georgia Tech before going pro, was drafted by the Los Angeles Lakers in 2007 and then traded to the Memphis Grizzlies.
He was picked up by the Washington Wizards in December 2008 but was suspended and later released by the NBA in 2010 after a gun-related incident involving teammate Gilbert Arenas.