There were no injuries, and the runway was cleared about an hour later, spokeswoman Arlene Salac said.
Three similar incidents involving Airbus planes have occurred since 2000, including two in the past three years, according to incident reports filed by the National Transportation Safety Board.
In January 2008, a passenger on an Airbus A319 operated by Northwest Airlines from New York to Detroit reported seeing a cowling flapping shortly after takeoff.
The flight continued, and, according to the NTSB report, half of the cowling fell off as the plane made its final approach to Detroit Wayne County Metropolitan Airport.
The other half fell off during landing and was contacted by another arriving plane, though the report didn't say whether the second plane was damaged.
In April 2007, another Airbus A319 operated by Frontier Airlines lost an engine cowling while taking off from Atlanta's Hartsfield-Jackson International Airport and had to return to the airport.
On an AmericaWest flight from Las Vegas to Columbus, Ohio, in June 2000, a cowling fell off the Airbus A319 on takeoff, prompting several passengers to alert flight attendants. The plane returned to the airport without incident.
All three times, the NTSB faulted mechanics and maintenance personnel for failing to secure the cowlings after routine preflight inspection.
Mary Anne Greczyn, an Airbus spokeswoman, did not comment on the previous incidents but said the company was investigating Monday's incident.
The Airbus A319 and A320 are part of the A320 family of narrow-body, single-aisle jets.