The shootout occurred when three federal officers approached the two suspects in the airport's terminal 2, which handles international and domestic flights. Two agents were killed at the terminal and another later died of his injuries in hospital.
The suspects, who remain at large, are believed to be part of a larger group of officials involved in a cocaine ring, Mexico's security ministry said in a statement.
Airport spokesman Jorge Gomez told Milenio that aircraft departures and arrivals continued normally after the incident.
Mexico City has seen relatively low murder rates compared to the rest of the country, where drug violence has killed around 55,000 people in the past five and half years.
But attacks have been creeping up in the capital and its surrounding neighborhoods, with more than 300 gangland killings recorded last year.
Mexico's airports and ports are busy areas for drug smugglers. So far this year federal police have seized more than 440 pounds (200 kilograms) of cocaine at the capital's airport, double the amount taken there last year.