Brown's ban will start with Sunday's game against the Dallas Cowboys. He will not appeal the suspension.
"I unknowingly took a supplement tainted with a banned substance and now have to deal with the consequences," Brown said in a statement on the team's website (houstontexans.com).
"I want to personally apologies to (the whole organization), my family, and to all the great and loyal Texans fans.
"I vow to learn from this mistake and be a better player and team mate because of it."
Brown, a first-round draft pick in 2008, joins team mate Brian Cushing on the sidelines after the linebacker was suspended four games in the offseason for the same offense.
(Reporting by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)