Jockey Brian Toomey is in an induced coma in hospital after surgery to reduce swelling on his brain following a fall at Perth racecourse on Thursday.
Lisa Hancock, chief executive of the Injured Jockeys' Fund, said Sunday's operation went well and the Irish rider was in "a stable condition".
"It is anticipated he will be kept sedated for a few days as his progress continues to be monitored," she said.
Toomey, 24, was on Solway Dandy when the horse fell in a hurdle race.
His parents Marian and Johnny, brother Sean, sister Aine and his aunt Margaret have thanked family and friends for their "huge support".
"Mrs Toomey would also particularly like to thank Dr Michael Turner for travelling up to Dundee on Saturday and the staff at Ninewells Hospital [in Dundee] for their fantastic round-the-clock care," added Hancock.
Toomey, who is attached to the yard of Kevin Ryan, is the boyfriend of the North Yorkshire trainer's daughter Amy, who was last season's champion apprentice rider.
A statement on behalf of the family and the Professional Jockeys' Association added: "Brian's girlfriend Amy Ryan would like to thank all family and friends and the racing fraternity for their texts and phone calls, especially Brian's close friends [jockeys] Brian Hughes and JP O'Farrell.
"Kevin Ryan would also like to thank his owners and staff for their support over the last few days."
Toomey has ridden 49 winners over the jumps since 2008 and has represented Ryan's stable at the Cheltenham, Aintree and Punchestown festivals.
His injury illustrates the dangers faced in jump racing, where jockeys fall on average one in every 16 rides.
Popular amateur jockey JT McNamara was paralysed after suffering spinal injuries in a fall at the Cheltenham Festival in March.
However, some serious incidents have resulted in a happy outcome, with Peter Toole almost fully recovered two years on from a head injury sustained at Aintree's Grand National meeting which left him in a coma for 11 days.