Recordings that emerged last month feature the boy together with his certified air traffic controller father, BBC News reports.
The child is heard saying: "JetBlue 171 contact departure." A pilot then responded: "Over to departure JetBlue 171, awesome job."
An adult is later heard laughing and adding: "That's what you get, guys, when the kids are out of school."
A Federal Aviation Administration (FAA) statement read: "Pending the outcome of our investigation, the employees involved in this incident are not controlling air traffic.
"This behaviour is not acceptable and does not demonstrate the kind of professionalism expected from all FAA employees."