Smith already appealed the suspension and lost, according to NFL.com's Ian Rapoport.
In July, Smith received concurrent 12-day jail sentences for weapons and DUI charges. Smith was also placed on three years' probation and asked to serve 235 hours of community service and pay a $2,000 fine.
Smith, 24, pleaded no contest in May to three felony weapons charges and two misdemeanor counts of driving under the influence.
The linebacker will be allowed around San Francisco's facility during the suspension, according to Rapoport.
Smith was also arrested in September 2013 on suspicion of DUI charges and was admitted into rehab after deciding to take a leave of absence from football.
In April, Smith was taken into custody at Los Angeles Airport for reportedly making a fake bomb threat. No charges were filed.
Smith, 24, played in 11 games for the 49ers last season, recording 34 total tackles and 8.5 sacks. San Francisco drafted him in the first round out of Missouri in 2011.
The 49ers open the regular season Sept. 7 against Dallas. Smith will be allowed to return for the team's week 11 game against the Giants.
- Chris Johnson