The team said Smith had been placed on the reserve/non-football injury list following an arrest last week on charges of driving under the influence and possession of marijuana.
The move came after 49ers Chief Executive Jed York revealed Smith would enter a treatment facility with no timetable for his return following Sunday's 27-7 loss to the Indianapolis Colts.
Smith -- one of the NFL's premier pass rushers with 19 1/2 sacks last season -- crashed his car in San Jose, Calif., early Friday.
He also was arrested for drunken driving in Miami last year and has been named in two lawsuits stemming from a house party during which he was reportedly stabbed.
"I am taking a leave of absence to address my health," Smith said in a statement. "I am sorry that I have affected my team, my family and the organization. I will do everything in my power to handle this situation the best way possible. I appreciate the support of the 49ers and our fans."