The reason is that the 65-year-old was filmed beating a horse several times with a tree branch.
Todd, who took two straight Olympic golds in the individual field competition in 1984 and 1988 on the horse Charisma and competed in the Olympics as late as 2016, is training in Wiltshire in the south of England and is suspended for the time being.
"While the investigation continues into the circumstances of the incident, Sir Mark will not be able to compete with horses in the UK or internationally," the BHA wrote in a statement.
Todd has apologized for his actions.