The young Scot, who is making his debut in the event, will also take on two other Americans, Kevin Na and Adam Long, in the round-robin stage at Austin Country Club.
Na, a five-time PGA Tour winner, is MacIntyre’s first opponent on Wednesday in the last of 32 matches starting at 8.11pm UK time.
The 24-year-old from Oban then faces Masters champion Johnson at 6.32pm UK time on Thursday before concluding the knock-out phase against Long, who won the 2019 Desert Classic on the PGA Tour, on Friday.
The time for the latter has still to be determined and will be based on how groups are standing after the opening two matches.
It will take a monumental effort for MacIntyre to eclipse Johnson over the three matches and progress to the last 16 as the group winner, but, on the other hand, it’s an exciting opportunity.
"Nothing changes,” said MacIntyre of hearing about his group. “There are still three guys to get past. It's a big draw, but it's where you want to be so no complaints.
“I'll mark their cards and they'll mark mine and we will see who goes through in the end."
If he can pull it off, MacIntyre would then meet the winner from a group comprising Dundee-based Frenchman Victor Perez, Sungjae Im, Marc Leishman and Russell Henley.
Defending champion Kevin Kisner has world No 2 and recent Players’ Championship winner Justin Thomas in his group, which also includes 2010 Open champion Louis Oosthuizen and Matt Kuchar.
One of the most intriguing groups is an all-European line up of English trio Tyrrell Hatton, Lee Westwod and Matt Wallace and Spaniard Sergio Garcia.
Rory McIloy, the 2015 winner, has Ryder Cup team-mate Ian Poulter in his group.
Full draw (with seedings in brackets)
Group 1:  Dustin Johnson  Kevin Na  Robert MacIntyre  Adam Long
Group 2:  Justin Thomas  Louis Oosthuizen  Kevin Kisner  Matt Kuchar
Group 3:  Jon Rahm  Ryan Palmer  Shane Lowry  Sebastian Munoz
Group 4:  Collin Morikawa  Billy Horschel  Max Homa  J.T. Poston
Group 5:  Bryson DeChambeau  Tommy Fleetwood  Si Woo Kim  Antoine Rozner
Group 6:  Xander Schauffele  Scottie Scheffler  Jason Day  Andy Sullivan
Group 7:  Patrick Reed  Joaquin Niemann  Christiaan Bezuidenhout  Bubba Watson
Group 8:  Tyrrell Hatton  Lee Westwood  Sergio Garcia  Matt Wallace
Group 9:  Webb Simpson  Paul Casey  Mackenzie Hughes  Talor Gooch
Group 10:  Patrick Cantlay  Hideki Matsuyama  Carlos Ortiz  Brian Harman
Group 11:  Rory McIlroy,  Cameron Smith,  Lanto Griffin,  Ian Poulter
Group 12:  Tony Finau  Jason Kokrak  Will Zalatoris  Dylan Frittelli
Group 13:  Viktor Hovland  Abraham Ancer  Bernd Wiesberger  Kevin Streelman
Group 14:  Daniel Berger  Harris English  Brendon Todd  Erik van Rooyen
Group 15:  Matt Fitzpatrick  Matthew Wolff  Corey Conners  Jordan Spieth
Group 16:  Sungjae Im  Victor Perez  Marc Leishman  Russell Henley