Griffin is expected to make a full recovery from the injury, which sources say was suffered during the playoffs. However, doctors advised him to sit out international competition this summer for precautionary reasons.
Griffin has continued to work out this summer in Los Angeles with teammate DeAndre Jordan and former Laker and Clipper Sasha Vujacic.
Both Griffin and Minnesota forward Kevin Love withdrew from the training camp last week, which left Team USA thin in the front court and prompted the late addition of Atlanta's Paul Millsap to the camp.
In a statement, USA Basketball said Love was unable to participate "because of his current status," a thinly veiled reference to the trade talks that have dragged on since June.