The striking educators descended on the capital this week from across the country, staging sit-ins at the chamber of deputies and senate that forced lawmakers to move their debates in a convention center.
Airport director general Alfonso Sarabia said many travelers were late for planes Friday when they were forced to take the metro to reach the two terminals after the teachers blocked road access. Some passengers walked down the boulevard leading to the airport.
But the national security council said the airport operated normally without flight delays despite the protest.
Some airlines offered to change tickets for free to people who arrived late because of the protest.
The teachers were still blocking the main access road late Friday after police took control of secondary roads, where they set up checkpoints allowing bus and people with plane tickets to go through in taxis, an airport official told AFP.
The official, who requested anonymity, said the airport may consider diverting flights to other airports "if this situation continues for several days."
Jesus Rodriguez Almeida, the city's public security secretary, said 1,700 police officers were deployed to guard the terminals, warning that operations there would only be interrupted "over my dead body."
Federal police said it had transported 2,500 people from a metro station to Terminal 1 and would continue the service until the blockade is lifted.
Opposition lawmakers have criticized Mexico City Mayor Miguel Angel Mancera's handling of the protests, but he countered Thursday that his government respects the right to protest and that his priority was to prevent clashes "at all cost."
President Enrique Pena Nieto pushed through Congress changes to the constitution in December in order to put education, which was in the hands of powerful unions, back under government control and require teachers to undergo mandatory performance appraisals.
Lawmakers are now debating legislation that would implement the new laws, which have prompted protests and strikes in the southern states of Michoacan, Guerrero and Oaxaca in recent months.
The teachers say the tests should only be used to help them improve, not to fire them or decide promotions. The union that called the protests urged lawmakers to suspend the debate and enter into negotiations with teachers.
More than 70,000 teachers went on strike in southern Mexico, leaving more than one million children without classes at the start of the school year this week.