Smith is FSU's leading tackler with 60 on the season, and leads the ACC with 10.2 tackles per game. He also has one sack and a forced fumble.
Linafelt reports that Smith has a neck strain and initially thought he could play before being ruled out.
The Seminoles will also be without linebackers Jacob Pugh, EJ Levenberry and Ukeme Eligwe against the Cardinals, according to Linafelt.
No. 2 Florida State (7-0) and Louisville (6-2) kick off at 7:30 p.m. ET Thursday.
- Molly Geary