Police arrested the unnamed pair at the travel hub after the woman reportedly fell over in the departure lounge.
Following the arrest, the pair were taken to a local police station while their three children were handed over to social services.
Police have said both parents were charged with being intoxicated while in charge of a child.
The Royal Gibraltar Police confirmed the arrest in a statement: “A 54-year-old man and a 53-year-old woman, both British nationals, were arrested yesterday evening for being intoxicated whilst in charge of a child.
“Police were called to the Gibraltar International Airport to assist a GHA ambulance crew who were having difficulties with a female passenger who had fallen over in the departures lounge.
“On arrival, the officers noted that the female and her husband, who were due to fly out later that night with their three young children, were both intoxicated.”
Local media have reported the woman who fell over in the depature lounge was also charged with criminal damage.
The family were thought to be due to fly out of the island but their destination has yet to be revealed.
Both the man and the woman were expected to appear in court today.
Gibraltar airport is known for having one of the strangest runways in the world – split betweent the island’s busiest raods.
The street closes whenever a plane lands or departs with only a pair of flimsy barriers separating a jet from those on their daily commute.