A Boeing 737 had to quickly brake when the plane's engine looked like it was starting to fall apart ... and the whole ordeal was caught on video.

The Southwest Airlines flight, heading from Denver to Houston, took off Sunday morning ... when some of the passengers noticed a piece of metal ripped off the side of the plane and flapped around as the plane began its takeoff.

Check out the video ... the engine cowling covering the sides of the giant turbine flies up, seemingly only held together by a few strands of stray metal -- at first, not slowing down the jet one bit.

However, once the piece breaks away and flies off, the pilots slowly rolled the plane to a halt with the turbine almost completely exposed.

Southwest tells TMZ ... the passengers onboard got off the plane safely and boarded another aircraft -- landing in Houston about three hours after their original estimated arrival time. The airline says it's looking into the mechanical failure.

This is just the latest in a series of mechanical headaches Boeing's facing ... remember, just last month a United Airlines Boeing 777 lost a tire right as it took off, smashing several cars below.

And, of course, the door of a different plane blew out during one flight, forcing the 737 Max 9 to make an emergency landing in Portland ... so, this latest issue seems more of the recent same for the plane-producing giant.

All's well that ends well, we guess ... though some people might be rethinking upcoming travel.