Authorities said they had arrested 26-year-old Esteban Santiago, an Army National Guard veteran who served in Iraq and was honourably discharged last August from the Alaskan National Guard, in connection with the shootings. His brother said he had been receiving psychological treatment recently.
US officials said Santiago was a passenger on a Delta flight from Anchorage via Minneapolis and carried a checked gun, which he was said to have loaded in the bathroom before allegedly opening fire in the baggage claim area of terminal 2.
His gunfire killed five people and wounded eight, but a total of 37 other people suffered minor injuries after the incident, including panic attacks and diabetic-related issues, according to the Broward Sheriff's office.
They added that the number of people injured was a "fluid situation" and could not say how many people were critically injured.
Florida governor Rick Scott said the shooting was an "evil, despicable act" and called for prayers for the victims in hospital, many of whom are fighting their lives.
He told reporters that now was not the time to be "political" and discuss gun rights. He reportedly did not phone President Barack Obama, but rather phoned President-elect Donald Trump.
"I am going to do everything I can to keep everyone safe," he told CNN. "I'm not going to tolerate this."
Mr Obama said it was too early to say whether the incident was an act of terrorism. He said that he was "heartbroken".
"These kinds of tragedies have happened too often during the years I've been president," he said.
"The pain, the grief, the shock that they must be going through is enormous."
Barbara Sharief, mayor of Broward County, said the shooter acted alone.
"We have no evidence at this time that he was acting with anyone else. [The suspect] is currently in custody and we're investigating."
Investigators have not yet determined a motive for the shooting.
A witness told NBC New that the shootings the gunman had laid down "spread eagle", and was on the ground for "10 to 15 minutes" before the first police officers arrived.
Eyewitness Mike Starobinsky told ABC News that he heard "popping noises" in the terminal. He grabbed his children and took them to meet family in the neighbouring Terminal 3 when he saw a victim outside "bleeding profusely".
Mr Starobinsky took a photograph of the scene outside the terminal that showed a woman giving aid to the bloodied victim.
John Schilcher told Fox News that the "firing went on and on".
Mr Schilcher, who was with his mother-in-law and his wife, said the terminal went "eerily quiet" as the gunman reloaded his weapon.
Ari Fleischer, a White House press secretary during the George W Bush administration, was at the airport at the time of the shooting. He tweeted early reports of the incident.
"I'm at the Ft Lauderdale Airport. Shots have been fired," he wrote. "Everyone is running."
He later added: "All seems calm now, but the police aren't letting anyone out of the airport – at least not the area where I am."
Passengers and employees were evacuated from the terminal onto the tarmac, but some later slowly returned to the inside of the airport. All flights to the airport were being diverted.
"We were told to hit the deck and we stayed there until we were given the green light to leave," a traveller who was at the airport, Bob Foster, told MSNBC. "Needless to say, everybody's pretty shaken up."
Airport officials tweeted: "All services are temporarily suspended at #FLL. Please contact your air carrier about your flight information."
Agents from the Bureau of Alcohol, Tobacco, Firearms and Explosives were present to assist state and local law enforcement in their investigation.
Police carried out a controlled explosion on a "suspicious package" left near the railroad tracks, and warned passersby to not be alarmed.
Ft Lauderdale/Hollywood International Airport sees some 73,000 passengers pass through daily.