He challenges people at home to make the most "badass bandito bandana" they can.
His mask-making video also sparked a tutorial request from Late Show host Stephen Colbert.
Colbert had the actor on his talk show via a video conference call, and the Dallas Buyers Club star told him how he stumbled across the kooky character.
"I found him, I was out hiking on our property and came across a guy nailing a most wanted sign into my oak tree," the actor jokes.
"He told me what he was up to, he's a bounty hunter and he's out to catch the 'corona-v', reminding everybody to put a mask on if they've got to leave home."
McConaughey teaches the host how to fashion his own mask - and Colbert almost nails it.
His other videos posted to his Twitter account include reminders for his followers to take the necessary precautions to help eradicate the virus, and to stay home and practise social distancing.