The 24-year-old linebacker, one of the best in the NFL at sacking quarterbacks, was suspended on Friday.
Trent Baalke, the 49ers general manager, said it was a decision the franchise had expected.
"Our organisation has known this decision would come and we have prepared for it as a team," Baalke said in a statement.
"Aldon has taken responsibility for his actions and has continued to show growth personally and professionally.
"We will continue to support him, but it is time to put this matter behind us and focus on the season ahead."
Smith misses matches against the Dallas Cowboys, Chicago Bears, Arizona Cardinals, Philadelphia Eagles, Kansas City Chiefs, two against the St Louis Rams, Denver Broncos and the New Orleans Saints.