Davis, who made seven catches for 70 yards with a score in 10 games for Washington last season, will be banned effective immediately, the league said.
The tight end issued a statement through the NFL Players Association saying he has "worked very hard to eliminate marijuana from my life" since testing positive for the drug in 2011 and asserted the latest suspension was the result of taking a dietary supplement that contained a banned substance.
"I now know that supplements are not regulated by the FDA and may contain banned substances," he said. "The NFL policy is strict, and not knowing that a supplement might contain a banned substance doesn't excuse a violation of the policy."
Davis vowed to stay in football shape and hopes to "get back on the field to contribute to a team's success next season."