Three sources have told Reuters that the carrier will only get about 20 737 MAX planes this year.
It had originally expected 85.
The shortfall comes as Boeing grapples with the fallout from January's midair blowout on a plane operated by Alaska Airlines.
No one was killed in the incident, but it raised fresh concern over quality controls at the aerospace giant.
The Federal Aviation Administration has since capped output of MAX planes at 38 per month.
But production appears to be well short of even that level.
The problem affects many airlines that had jets on order.
But Southwest has an all-Boeing fleet, making it especially vulnerable.
In a statement, the airline said it was in touch with the jetmaker over delivery schedules.
There was no comment from Boeing.
Southwest had planned to increase capacity by 6% this year, but last month warned that figure could now be slashed.
It's frozen hiring of new pilots, and may now be forced to keep older planes in service.
That means doing heavy maintenance on aging jets, with costs running to many millions.
Other airlines to face trouble include United, which has also now paused pilot recruitment.
