One suspicious package was found in the terminal, and another was found in the parking garage, CNN reported.
The FBI in Jacksonville was involved in the investigation.
Police said they contained a device "that had to be rendered safe," The (Jacksonville, Fla.) Times-Union reported.
Airport spokesman Michael Stewart said passengers could return to the terminal to pick up their luggage and check with airlines for morning flight information.
Witness Jennifer Lee told WJXT-TV, Jacksonville, she saw a man taken into custody at the security checkpoint.
"My colleague and I were coming through security, and all of a sudden they stopped everybody that was in security," Lee said. "We looked a couple of lanes over and they were arresting a gentleman in sunglasses. Originally they told us to stand there. Then they started to yell at us to leave."
Another witness said he saw a different man who had disembarked from a flight being tackled by authorities who told him to drop his bag. That man was taken into custody as well.
The Jacksonville Sheriff's Office bomb squad was called to the scene at about 6:30 p.m. EDT; 50 police cars and several ambulances also responded, the TV station said.
Flights were delayed, gates were closed and some witnesses said they had loved ones who were stuck in planes on the runway that were unable to reach their intended gates.
Southwest Airlines said two flights had been diverted to Orlando, Fla.
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