The triple major winner picked up the injury while working in the gym earlier this week.
The 43-year-old Irishman started the first round with a bogey and a par and decided to withdraw after playing a shot out of the rough at the third.
"My shoulder improved quite a bit overnight," Harrington told reporters. "A lot of times when I've had injuries in the past I have got better as the round has progressed.
"There are a lot of times when you might carry an injury into a tournament and you go out having a little bit of an adrenaline release but today it went the other way for me.
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"My shoulder just got worse. The pain was exceptional and it just felt horrible."
Harrington is ranked 83rd and needed a good result this week to get back among the world's top 60 in order to qualify for the second major of the season at Chambers Bay in Washington State.
He now plans to enter Monday's 36-hole U.S. Open qualifying event at Walton Heath on the outskirts of London.
(Editing by Tony Jimenez)
