Khairuldeen Makhzoomi, 26, who came to the US from Iraq as a refugee, told the he was removed from the flight in California earlier in April after speaking to his uncle on the phone in Arabic.
He said he had been telling his uncle about an event he had attended that had included a speech by United National Secretary-General Ban Ki Moon.
The New York Times reported Mr Makhzoomi said he told his uncle he was able to ask the Secretary-General a question about Islamic State and then noticed a passenger sitting near him get up and speak to one of the flight attendants.
"That is when I thought, ‘Oh, I hope she is not reporting me,’ because it was so weird," he said.
Mr Makhzoomi was then approached by an Arabic-speaking employee who asked him why he had been speaking Arabic on the plane.
"I said to him, ‘This is what Islamophobia got this country into,’ and that made him so angry," he said.
"That is when he told me I could not go back on the plane.”
Law enforcement officers then arrived and Mr Makhzoomi was escorted back into the terminal and searched and then questioned by three FBI agents about his family.
The New York Times reported one of the FBI agents said the Southwest employee was upset about Mr Makhzoomi's anti-Muslim bias comments and that the passenger who complained had heard him talking about martyrdom and using jihadist phrases.
An FBI spokeswoman told the New York Times no further action would be taken against Mr Makhzoomi, who was able to book a new flight with Delta Air Lines.
Southwest Airlines spokeswoman Brandy King told the New York Times the passenger had complained of hearing Mr Makhzoomi making "potentially threatening comments".
"We regret any less than positive experience a customer has onboard our aircraft," the company said in a statement.
"Southwest neither condones nor tolerates discrimination of any kind."
Mr Makhzoomi is seeking an apology from Southwest Airlines for his treatment.
"My family and I have been through a lot and this is just another one of the experiences I have had," he said.
"Human dignity is the most valuable thing in the world, not money. If they apologised, maybe it would teach them to treat people equally."
