"Just wanted to let everybody know that I am fine but will be going into surgery tomorrow morning," Floersch wrote on Twitter.
"Thanks to the @fia and @hwaag_official @MercedesAMGF1 who are taking great care of me. Thanks to everybody for the supporting messages. Update soon."
Japanese driver Sho Tsuboi, who Floersch crashed into, was taken to hospital with back pain.
Race organisers confirmed two photographers and a marshal were also in hospital.
Pole-sitter Daniel Ticktum was leading the race when it was stopped.
(Reporting by Hardik Vyas in Bengaluru; Editing by Toby Davis)