A day after being hit with the ban, Smith released a statement through the NFL Players Association expressing regret for substance abuse and personal conduct policy violations.
Smith has been one of the NFL's top pass rushers over the past three seasons, making 42 quarterback sacks in that span, the second-most of any player.
In July, Smith was sentenced to 11 days in jail and placed on three years of probation on weapons and drink driving charges from a 2013 incident.
"I apologize to my teammates, coaches, the entire 49ers organization and 49ers fans for not being able to contribute on the field for the next several weeks," Smith said.
"Over the last year, I have learned a lot and I'm working hard to grow from my experiences.
"I will be at work daily to participate in all permitted work activities, and to support my teammates, just as they have supported me."
Smith took a voluntary leave of absence last season, missing five games to deal with a substance abuse issue.
He will be able to return for the 49ers in November in a game against the New York Giants.