Vols coach Butch Jones said Tuesday that Smith won't practice this week.
"There isn't a time frame on it," Jones said. "He could be ready for Georgia, but we'll wait and see."
Smith has caught 10 passes for 135 yards, including a 40-yarder for a touchdown, Saturday in a 34-10 loss at No. 4 Oklahoma. Receiver Von Pearson also has a high ankle sprain, which prevented him from playing against Oklahoma.
Tennessee also is dealing with injuries at tight end. A bruised knee kept Ethan Wolf from playing Saturday, and Daniel Helm has a sprained ankle. Jones expects both Wolf and Helm to play against Georgia.