Lawrie missed last week's Buick Classic because of the injury. He said he received extensive treatment but was advised to skip the Open.
He needs further rest and treatment and wants to be "completely cured" before returning to the tour, Lawrie said in a statement released by IMG.
He will be replaced in the 156-man field by Don Pooley, who was the odd man out when 13 players competed for 12 spots in a playoff at the sectional qualifier in Rockville, Md. Pooley was the first alternate.
Lawrie hopes to return to a full schedule within the next few weeks and be ready to defend his British Open title at St. Andrews, July 20-23.
The Scottish golfer, who won at Carnoustie last year in a playoff againstJean Van De Velde and Justin Leonard, had been grouped with Jack Nicklaus and David Gossett in the first and second round for Pebble Beach.
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