Pin had withdrawn from the Formula Regional European Championship by Alpine's second Spa-Francorchamps race last weekend after feeling some discomfort.
The Frenchwoman has now posted a video on social media announcing that she will be unable to race at Le Mans, where she should have shared the Iron Dames' #85 Lamborghini Huracan GT3 Evo 2 in the WEC's LMGT3 class with team-mates Sarah Bovy and Michelle Gatting
She will also sit out the next FRECA round at Zandvoort on 8-9 June.
"After further medical checks, we found out that I have fractured ribs," Pin said, with the origin of the injury still unclear. "Obviously, it means that I need time to heal.
"So we have made the difficult decision with my team to not race in the 24 Hours of Le Mans and the FRECA races in Zandvoort.
"This decision is tough and sad, especially since Le Mans is one of the biggest races of the year, and for me, it's a very special one.
"I was looking forward to driving there and sharing that week with all of you and, of course, my team. But I need to do what is best for myself and the Iron Dames."
Rahel Frey will stand in for Pin at Circuit de la Sarthe, with the Swiss veteran having already raced there with Iron Lynx/Iron Dames alongside Bovy and Gatting in previous years, achieving a best result of fourth in the LMGTE Am category in 2023.
Pin is otherwise having a very busy 2024 season, having joined the Mercedes young driver academy back in January.
Having previously focused on sportscar racing, Pin switched her attention to single-seaters, joining powerhouse Prema Racing. She took one victory during an incomplete campaign in the Formula 4 UAE championship and went on to become an F1 Academy frontrunner, before making a more arduous FRECA debut.
Although she's still racing in the WEC with Iron Dames, Pin recently clarified that she would focus solely on single-seaters from 2025 onwards.
The 20-year-old is planning on being back on track at the F1 Academy's Barcelona round on 21-23 June.
