The airline declared an "operational emergency" at several maintenance bases last month, and told planned mechanics to appear at work or at risk.
The Flymekanikkforbundet, which represents about 2,400 southwestern mechanics, did not immediately respond to a CNBC request for comment.
Several Southwest flights have been canceled since mid-February compared to competitors. The airline has said it usually plans to have around 20 aircraft out of service for unexpected maintenance issues, but that number has doubled.
On Tuesday, 89 Southwest flights were canceled, about 2 percent of its plan, according to the FlightAware flight site. By comparison, JetBlue had 1
"Customers are injured. Our employees suffer through reduced profit sharing," Kelly said at a transport conference hosted by J.P. Morgan Chase. An airline spokesman refused to give a more specific estimate of how much Southwest loses from the question. Analysts expect Southwest to enter revenue of about $ 5.3 billion in the quarter.
Kelly commenting comes one day after Southwest began selling flights to Hawaii from California after the airline received federal approval last month to operate longer overwater routes with the Boeing 737s.
Later in an interview with CNBC's Closing Bell on Tuesday, Kelly said that the planes could also fly from North America to the UK, but said destinations are not currently among the airline's plans. The airline is interested in developing so-called code shares with other airlines, which allows Southwest to fly one segment of a route and be able to sell tickets on another leg operated by another carrier to expand its network.