Officials said McMurray bumped and spun the car of Matt Kenseth in the cool-down lap after the Sunday race. NASCAR said McMurray's actions were "detrimental to racing."
McMurray's probation runs through the end of August.
The two drivers battled for position for several laps. Both said they made bump-and-run manuevers to make passes.
"You can't really get out and punch somebody in our sport. I wanted him to know I was mad," McMurray said. "This place is so easy to get mad. I was just shocked Matt did that. He's really a good racer, but lost his cool today."
McMurray finished eighth and Kenseth fifth in the race won by Kurt Busch.