The league announced the suspension Wednesday.
Washington made the Pro Bowl as an alternate last season, when he led the Cardinals with 140 tackles, 110 of them solo. He had 9 sacks, 14 tackles for loss, 2 forced fumbles, 1 interception, 1 fumble recovery and 6 passes defensed.
Washington's nine sacks were the most by an NFL inside linebacker. Washington also led the team in tackles in 2011.
He is eligible to participate in all preseason practices and in preseason games.
A second-round draft pick out of TCU in 2010, Washington had signed a six-year contract in September. He will have a $10 million option bonus due by the last day of the 2013 league year.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.