The Dallas-based airline expects its revenue per available seat mile, a key industry metric of how much an airline generates for each seat it flies a mile, to grow 2 to 3 percent compared with an earlier forecast of as much as 4 percent.
Southwest shares were up 1.5 percent in late-morning trading.
The Federal Aviation Administration grounded Boeing 737 Max planes earlier this month following two fatal crashes. Investigators have noted "clear similarities" between an Ethiopian Airlines crash of a 737 Max on March 10 and another deadly crash of that model of plane in Indonesia in October.
Southwest operates an all-Boeing 737 fleet, and has 34 737 Max 8 planes in its fleet of about 750 aircraft. The carrier said it expects to have canceled 9,400 flights in the first quarter, 2,800 of them because of the grounded Max planes.
Southwest said its operating costs, excluding fuel, in the quarter will likely rise 10 percent from a year ago, up from a previous forecast of a 6 percent year-over-year increase.
The airline said it expects to lose $150 million in revenue in the first quarter of 2019, up from a February estimate of $60 million, due to weather-related cancellations, maintenance issues, weak leisure-travel demand and the Max groundings.
It's a small amount compared with the $5.3 billion in revenue analysts expect Southwest to generate in the first three months of 2019, but investors are focused on how the suspension of the 737 Max planes will financially impact airlines.
American Airlines earlier this week said it planned to cancel about 90 flights a day through April 24 due to the Max grounding. That period encompasses the busy Easter and Passover travel period.
Boeing is scheduled on Wednesday morning to outline the changes to a piece of software that Indonesian investigators have indicated played a role in the Lion Air crash in October.
"Due to the current uncertainty regarding the duration of the Max groundings and any requirements for reinstatement of the aircraft into service, it is difficult for the company to forecast the impact of the MAX groundings beyond first quarter 2019," Southwest said.
As of March 13, Southwest said it had 41 deliveries of Max planes scheduled for this year.
Southwest reports first-quarter earnings in late April.