Davis was arrested at the Hawaiian Airlines check-in counter when, after being asked security questions about his luggage by an attendant, turned to a female companion and allegedly asked her, "Did you pack the explosives?"
The 24-year-old was taken into custody by LAX police and released from jail after posting $15,000 bond. The woman with Davis was not arrested, police said. Davis' preliminary court hearing is scheduled for May 3.
TMZ first reported Davis' arrest.
"The Packers are aware of the matter involving Trevor Davis," the Packers said in a statement. "We are in the process of gathering more information and will refrain from making any further comment as it is an ongoing legal matter."
The third-year wide receiver has appeared in 27 games over the last two seasons for Green Bay. Davis, selected by the Packers in the fifth round of the 2016 NFL Draft out of Cal, has eight career receptions for 13 yards. Phase 1 of the Packers' offseason program begins next week.
Davis could be subject to potential NFL discipline under the league's personal conduct policy.