The punishment was announced Monday.
Culliver will sit out Washington's Week 2 game Sunday against the visiting St. Louis Rams.
The league did not say exactly why Culliver was suspended. He was arrested in March 2014 on suspicion of felony hit-and-run and reckless driving.
The Redskins signed Culliver as a free agent in March after he spent four seasons with the San Francisco 49ers.
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