Those shot dead were trying to arrest the pair, who were suspected of being part of a cocaine trafficking ring.
Eyewitness Israel Lopez told the Associated Press news agency: “We were in the food court, and some policemen came in and started shooting at another policeman who was on the floor.”
Authorities have identified the two suspects. However, the gunmen escaped and are now being hunted down.
Though traffickers use the Central American capital’s main airport to move drugs, money and illegal migrants, violence related to drug trafficking seldom occurs in passenger areas.
Cops have seized 440lb (200kg) of cocaine at the airport so far this year.