Three to eight flights on American Airlines, U.S. Airways, Delta Air Lines and Alaska Air Group have been postponed so far, Richard Jimenez, a representative for Mexico City's international airport told Reuters.
"The decision not to fly from Mexico City has been made by these airlines, but the airport is in operable conditions," Andres Gomez, another airport representative, said on local television.
Mexico's leading airline AeroMexico suspended flights briefly Thursday morning, but resumed operations less than an hour later.
The volcano Popocatepetl in the central state of Puebla has been more active this year, prompting officials to raise warning levels but have so far ordered no evacuations.
Officials have kept the volcano's risk level on hold at "yellow," the second highest on the four-color spectrum, indicating that there is more activity than usual but no threat of eruption, national emergency services coordinator Luis Felipe said on Twitter.
On Thursday, ash fell on communities adjacent to the volcano, nicknamed Don Goyo, and reached southern neighborhoods of Mexico City.
There is no evidence of volcanic ash in the airport's immediate vicinity, it announced through its Twitter account. Volcanic ash can damage jet engines.
Mexico City's airport serves more than 29 million people a year and oversaw 174,511 takeoffs and landings between January and June.