Geiselman's condition after the wipeout is unclear. The incident happened at Pipeline, two days before the famous beach hosts the last round of the World Surf League.
The Pipeline Masters will decide whether Fanning wins a fourth world crown.
The Australian leads a tight championship race, with five other surfers in contention.
It has been a tumultuous year for Fanning - in July, he was competing in the final of the WSL event at South Africa's Jeffreys Bay when a shark attacked him.
Fanning punched the shark, scaring it off, as compatriot and fellow finalist Julian Wilson paddled over to help. Also on Sunday, Australian big wave surfer Mark Mathews was taken to hospital with an injured shoulder after a big wipeout before his opening round heat of the WSL's Big Wave Tour event at the Maui break of Jaws.
-AAP