The Phoenix-bound jet which took off from San Francisco this week was forced to divert to Los Angeles International Airport after a woman gave birth soon after take off.
A spokesperson for the airline says the woman was aided by a doctor and nurse who happened to be on board.
Erik Scott, a Los Angeles Fire Department spokesman, confirms that paramedics boarded the aircraft and the mother and newborn were transported to hospital safely.
The plane was then taken out of service briefly for cleaning, causing some flight delays.
The Southwest spokeswoman is hopeful that the airline has a new customer for life.