Smith played in Sunday's game against the Indianapolis Colts following a DUI arrest he received Friday, the second of his career. It was reported that Smith was in possession of pills when police found Smith passed out in his car with his foot on the accelerator.
A series of reports indicated that Smith would receive treatment following the 49ers' Week 3 game and could enter a rehabilitation facility. York did not mention if the leave of absence is related to further treatment plans aimed to get the 23-year-old linebacker healthy.
Smith has amassed 37.0 sacks in three years for San Francisco after being selected in the first round of the 2011 draft out of Missouri. He recorded five tackles in Sunday's loss to the Indianapolis Colts.
The San Francisco 49ers will play the St. Louis Rams on Thursday Night Football. It will be the team's first game without Smith since he was drafted.