The FAA said the contractor did not put the planes on jacks to stabilize them. The work was done under the supervision of Southwest, which was responsible for ensuring that the procedures were followed, the FAA said.
After it put the airline on notice that the planes were not in compliance, the agency said, Southwest returned the jetliners to service and operated them on "numerous flights" in 2009.
The FAA later approved the repairs, after Southwest provided documentation that the work met safety standards.
This is the FAA's second proposed civil fine against Southwest for maintenance issues.
In 2008, the agency proposed a $10.2 million fine against the Dallas-based airline for operating 46 Boeing 737s on 59,791 flights in 2006 and 2007 without full inspections for fuselage cracks. Southwest, the second-busiest carrier at Philadelphia International Airport, disputed that fine, and after negotiations, it agreed to pay $7.5 million.
In a statement Monday, Southwest responded: "Safety is paramount and we always strive for full compliance with established and approved processes and procedures."
The repairs "were fully resolved some time ago," the airline said. "None of the items raised in the FAA letter affect aircraft currently being operated by Southwest."
The carrier added: "Southwest is committed to continuously making enhancements to our internal procedures, as well as improvements related to oversight of our repair vendors."
The FAA found that the contractor had applied sealant between the new skin panels, but did not install fasteners in all the rivet holes quickly enough for the sealant to be effective. "This could have resulted in gaps between the skin and the surface," allowing moisture and leading to corrosion, it said.
The FAA also said Southwest had failed to properly install a ground wire on water drain masts, a feature designed to prevent lightning strikes, on two of its Boeing 737s. The planes operated on more than 20 passenger flights after Southwest became aware of the discrepancies, but before the airline corrected the problem, the FAA said.
"Safety is our top priority, and that means holding airlines responsible for the repairs their contractors undertake," said U.S. Transportation Secretary Anthony Foxx.