Washington's latest offence was in relation to marijuana use, following on from another ban last season that saw him miss four games.
The 27-year-old also faced the prospect of a suspension for violating the league's personal conduct policy following his arrest on suspicion of aggravated assault in May 2013.
In a statement released through his agent, Washington said: "I recently learned that I had violations of the NFL Substances of Abuse policy related to marijuana.
"The policy is very strict, and I have chosen to take responsibility. I am committed to making changes in my life that will allow me to return to the NFL as soon as possible."
Washington led the Cardinals in tackles in 2011 and 2012, being elected to the Pro Bowl for the latter season.