Mr Kushner, a senior adviser to the president, had been receiving top-secret security briefings.
However, background checks into Mr Kushner had still not been completed, so he had interim clearance only.
He and other White House aides who have yet to receive permanent clearance will not now get top-secret briefings.
Mr Kushner, who is married to Mr Trump's daughter Ivanka, had access to the President's Daily Brief, a secret intelligence report.
