In the video shared online last week, the couple was seen facing each other and rallying a ball back and forth with tennis rackets near the airport entrance.
The video has attracted thousands of viewers, sparking a wave of criticism from the public for their "inconsiderate and disruptive" behavior, The Korea Times reported.
"What on earth are they doing?" a netizen wrote.
"The couple are really selfish and ignore public etiquette. Can't they see the other people?" another wrote.
Many also questioned why airport security guards had not intervened to prevent the couple from playing tennis inside the airport terminal.
However, airport officials claimed police have the primary authority to maintain order at the airport, according to The Korea Herald.
Police have launched an investigation to identify the couple.
Many presumed that they were foreigners, not Korean, Mail Business newspaper reported.
South Korea's Airport Facilities Act prohibits unauthorized occupation of facilities.