The couple with Belgian passports, who were about to board the plane from Tel Aviv to Brussels, left their babies behind.
The couple, who insisted on not buying new tickets for their children, left the baby in the check-in section of Ben-Gurion Airport and entered the passport queue.
The couple was taken into custody by the Israeli police after the incident was noticed.
Speaking to the Jerusalem Post newspaper, an airline company official said, "This is the first time something like this has happened to us. I can't believe this incident," he said.
It was announced that the condition of the baby, who was left on the control band, was good.
A spokesperson for the Israeli Police told CNN in a phone call that the issue appeared to have been resolved by the time the police arrived on the scene. "The babies were with their parents and no investigation is being conducted," he said.
