The actor, 43, was snapped looking shockingly frail Friday as he caught a flight from Los Angeles to New Orleans, where The Dallas Buyer's Club is set to begin filming Sunday.
McConaughey has lost 30 lbs. – and gained a mustache – for the role. In the movie, he plays a mid-1980s AIDS patient who seeks out experimental HIV drugs to prolong his life.
"Matthew starts shooting this weekend, so he's at his absolute lowest weight," a source close to the actor tells PEOPLE. "In a month, he'll begin to put it back on."
Around the time he gains the weight back, McConaughey will gain a new family member as well – wife Camila is set to deliver their third child this winter.
Reporting by ELIZABETH LEONARD