The inspections will focus on the fan blades, the FAA said.
"A small proportion of engines on our Boeing 737-800 fleet now require further inspections, following the issue of Airworthiness Directives by the FAA and EASA", a Qantas spokesperson said in a statement.
The company also recommended that fan blades with more than 20,000 cycles be inspected by the end of August - affecting an additional 2,500 engines.
Southwest, the nation's fourth-largest carrier by traffic, said around 40 flights were scratched while the airline checks engines on some of its Boeing Co.
The 43-year-old mother of two was sucked out of the broken window and pulled back inside by fellow passengers.
An investigation led by the National Transportation Safety Board led them to believe that one of the engine fan blades snapped on the Southwest flight.
A jet engine completes a cycle every time it completes an engine start, takeoff, landing, and full shut down.
Southwest immediately told authorities that the airline would commence an inspection of its entire fleet.
Southwest did not immediately say what proportion of the delays was tied to the engine inspections, or whether another problem was contributing to the widespread disruptions. Aircraft engine investigators found that the engine blade had undergone metal fatigue before breaking during that fateful flight.
In a statement released Sunday, Southwest said it notified customers Tuesday that there might be an impact because of the inspections.
USA federal safety investigators have said the naked eye can not detect the cracks and signs of metal fatigue that doomed the engine on Southwest Flight 1380. Manufacturer CFM International said in a statement last week it's assisting in the probe into the incident.