Smith had injections of platelet-rich plasma and hyaluronic acid Tuesday into the same knee in which he tore his ACL as a freshman in 2015.
"It does not look favorable for this week," Trojans coach Clay Helton said Wednesday night.
Smith did not play in USC's 31-20 win over Colorado on Oct. 13 because of a strained hamstring and left the 41-28 loss at Utah on Saturday in the first quarter because of the same injury. A four-year starter at inside linebacker, Smith leads the team with 47 tackles in six games and also has five tackles for loss with one sack this season.
Freshman Palaie Gaoteote and former walk-on Reuben Peters have played middle linebacker with Smith sidelined. Gaoteote has 20 tackles with 2 1/2 tackles for loss in two games since Smith sustained the hamstring injury.
Helton hopes to have Smith available for the road game at Oregon State on Nov. 3.
USC (4-3, 3-2 Pac-12) hosts Arizona State (3-4, 1-3) on Saturday.