The pair, who have not been identified, were checking in for a Ryanair flight from Ben Gurion International Airport to Brussels, Belgium on Tuesday with the infant.
It emerged that the baby did not have a ticket, and the couple headed off to board the flight -- leaving their child behind on the airline check-in counter.
The matter was referred to police, a spokeswoman for Ryanair told CNN in an email.
She said: "These passengers traveling from Tel Aviv to Brussels (31 Jan) presented at check-in without a booking for their infant. They then proceeded to security leaving the infant behind at check-in.
"The check-in agent at Ben Gurion Airport contacted Airport Security, who retrieved these passengers, and this is now a matter for local police."
According to Ryanair's website, "infants can be included in a flight reservation during the online booking process." When making plans to travel with an infant, a pop-up message appears on the site stating that there is a €25 ($27) charge -- or the local currency equivalent -- for each one-way flight the baby takes while sitting on an adult's lap. A seat must be paid for by separate arrangement if the adults want the baby to travel in a car seat.
The Israeli Airport Authority confirmed the episode to CNN and said in a statement:
"A couple and an infant with Belgian passports arrived for a flight at Terminal 1 without a ticket for the baby. The couple also arrived late for the flight, once the check-in for the flight was closed. The couple left the infant seat with the baby and ran toward the security checks at Terminal 1 in an attempt to reach the boarding gate for the flight."
A spokesman for Israel Police told CNN in a phone call that the matter appeared to have been resolved by the time police arrived on the scene. He said: "The baby was with the parents