The hearing will determine whether Todd engaged in "conduct prejudicial to the good reputation of horseracing in Great Britain by striking a horse multiple times with a tree branch," the BHA said Wednesday.
Last month, Sir Mark issued an apology saying it was an isolated incident that was out of character.
"I wholeheartedly apologise to the horse and all involved for my actions in this video clip," he said.
"One of the main things I preach is about establishing mutual respect between horse and rider and that patience and kindness is the best way to get results.
"I believe this is one of the main attributes along with a great empathy with animals that has enabled me to have a long and successful career in eventing. I am very disappointed in myself that I did not adhere to that in this case."
Todd is one of New Zealand's most famous Olympians. He competed in seven Summer Games from 1984-2016, winning gold medals in eventing in 1984 and '88 as well as three bronze medals.
He was given a knighthood in New Zealand's New Year's Honours in 2013 and has since become a racehorse trainer, based in Wiltshire, England.