The German's Finnish team mate Kimi Raikkonen sealed the Ferrari front-row lockout.
Hamilton, one point behind the German in the standings and a five-times winner in Hungary, will start from a disappointing fourth place on the grid and alongside his Finnish team mate Valtteri Bottas.
Hamilton had been hoping to match Michael Schumacher's all-time pole record and had set the fastest lap of the second phase of qualifying.
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(Reporting by Alan Baldwin, editing by Pritha Sarkar)
