The US carrier said engineers would be “looking for the same type of aircraft skin fatigue” in checks over the next few days.
About 300 flights have been cancelled as a result of the inspections.
Southwest Flight 812 from Phoenix to Sacramento, California, with 118 passengers on board, landed safely at a military base in Arizona on Friday.
There were no passenger injuries reported, despite the sudden drop in cabin pressure.
The airline said one flight attendant was slightly injured. (read more)