The former US Open champion will not take part over the weekend after shooting a six-over 78 for his second round.
McDowell blamed his inconsistent short game for his four bogeys and two double-bogeys on Friday, following a promising round of par on the opening day.
"You put everything in to the first Major championship of the year," McDowell told BBC Sport. "I double the first and walked off there feeling exactly how I don't want to feel.
"I managed to control myself and feel comfortable all day [on Thursday] and it only took two or three shots to get me out of my comfort zone. I threw so many shots away around the greens the last two days.
"It hurts right now."