The suspension came the same day the 2011 NFL Defensive Rookie of the Year's name emerged in court records as a potential witness in a Colorado murder case.
Miller will be absent during the first six regular-season games for the Broncos and won't be eligible to return until the team's Oct. 20 contest at Indianapolis.
"The substances of abuse policy requires everyone to comply with the rules. Although my suspension doesn't result from a positive test, there is no excuse for my violations of the rules," Miller said in a statement.
"I made mistakes and my suspension has hurt my team, Broncos fans, and myself. I am especially sorry for the effect of my bad decisions on others. I will not make the same mistakes about adhering to the policy in the future."
"Von is one of our teammates. He's part of the family," Broncos quarterback Peyton Manning said. "I certainly have his back. We support him 100 percent."
Miller, the second-overall pick in the 2011 draft, has racked up 132 tackles and 30 sacks in his first two NFL seasons.
Meanwhile, court records list Miller as a possible acquaintance of Dexter Lewis, accused of stabbing five people to death in October in a Denver bar, The Denver Post reported Tuesday.
However, Broncos spokesman Patrick Smyth told the newspaper there is no indication Miller met or knew anyone involved in the case.
Lynn Kimbrough, spokeswoman for the Denver district attorney's office, said Miller's name was mentioned during an investigation into the case and said he had been interviewed.
Lewis faces 16 counts, including first-degree murder, felony murder, robbery and arson, in the attack. Prosecutors said they will seek the death penalty against Lewis.
Couple mistakenly served bag of cash at McDonald's drive-thru
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'