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The 65-year-old, who now trains racehorses, was seen striking a horse several times while attempting to coax it towards a water jump in a cross-country schooling session.
"The chair of British racing's Independent Judicial Panel has today approved an application from the BHA that an interim suspension should be placed on the training licence of Sir Mark Todd following the emergence over the weekend of a video showing him striking a horse with what appears to be a branch," the BHA said in a statement.
The interim suspension means Todd, who trains in Wiltshire in Britain, will be unable to race horses in Britain or internationally until investigations into the circumstances surrounding the incident are carried out.
Todd, who won individual gold medals at the Los Angeles and Seoul Olympics and took a bronze medal in the team event at the London 2012 Games, has apologised for the incident.