De Jager was hurt in the Bulls' 39-33 Super Rugby win over the Sharks on Saturday and will not available before September, team officials said on Tuesday.
He joins his successor as SA Rugby Player of the Year, Malcolm Marx, on the sidelines for the four tests in June -- against Wales in Washington DC on June 2 and then three at home to England.
Marx has a hamstring injury.
South Africa will also miss Eben Etzebeth, who captained the team last year in the absence of Warren Whiteley, who is expected back from a knee injury in the coming weeks. Etzebeth is suffering from a long-standing shoulder injury.
(Reporting by Mark Gleeson in Johannesburg; Editing by Christian Radnedge)
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