The 31-year-old suffered the injury in the third quarter of Sunday's win at Atlanta when he hit quarterback Matt Ryan. It was Carolina's third straight win after an 0-2 start.
Short missed the final 14 games last season after suffering a partially torn rotator cuff in Week 2 against Tampa Bay. Rhule said it was not the same shoulder.
Short is in the fourth of a five-year, $80 million contract he signed in 2017 after having 23.5 sacks during a three-year span. He has since had only three sacks, all in 2018, when he started 14 games.
The injury will put added pressure on rookie first-round draft pick Derrick Brown, a former Auburn player picked seventh overall.
Rhule said the Panthers likely won't be in the market for another starting tackle, noting they could use a three-man rotation the way they have in recent weeks with end Efe Obada having the flexibility to move inside.
Meanwhile, running back Christian McCaffrey was not at practice despite being eligible to return from injured reserve after missing three games with a high ankle sprain. Rhule said McCaffrey "won't be activated as of right now," making him highly doubtful to return against the Bears.