The Las Vegas Sun reported Thursday the "no show" policy would apply to reservations made after May 10 involving flights with departure dates on or after Sept. 13.
There also would be several exceptions, including cancellations that were caused by sever weather and tickets sold to military personnel and senior citizens.
The airline reported Thursday it took in record revenues of $4.08 billion in the first quarter of the year, up from $3.99 billion in the first quarter of 2012.
Earnings for January through March came to $59 million or 8 cents per share. In the first three months of 2012, earnings came to $98 million or 13 cents per share.
The increased revenue came from various sources, including adding six seats to the carrier's Boeing 737 jets, adding a new fee for open premium boarding positions and increasing the prices of EarlyBird Check-In, the newspaper said.
"Passenger revenues were boosted significantly by continued progress on the AirTran integration, fleet modernization efforts and the Rapid Rewards loyalty program," Southwest Chairman and Chief Executive Officer Gary Kelly said in a statement.