Jennings and Bain have been released on bond, the sheriff's office told SI.com.
All three players have been suspended, head coach Les Miles said in a statement.
The three players are accused of entering an LSU student's apartment on Sunday and taking items that had allegedly been stolen from Jennings a week earlier, Louisiana newspaper The Advocate reports, citing a police report. There were at least three other men with the trio of football players during the incident, the report says.
Jennings was LSU's starting quarterback last year and Thomas was a starting cornerback before he suffered a season-ending injury. Bain played in 10 games as a backup last season and made six tackles.
The arrests come just hours after LSU defensive tackle Trey Lealaimatafao was arrested on simple battery and simple robbery charges. Lealaimatafao was allegedly involved in a bar fight in which he beat a male victim unconscious, punched the victim's girlfriend in the face and took items from the victim's pockets. He was subsequently suspended from the football team.
- Dan Gartland