Ingmar de Vos, president of the FEI, said he was “very shocked and disappointed” when he saw the video of Dujardin whipping a horse’s legs.
The footage shows Dujardin, 39, hitting a horse with a long equestrian whip.
Whips are used in all equestrian disciplines and when employed as a training aid should be utilised lightly to communicate with the horse.
De Vos told BBC Sport: “We have many riders, we have many athletes, many horses in our sport, so it is only a very low percentage, but every case is a case too much.
“So that is why we need to constantly educate our athletes and their entourage because what was allowed 30 years ago or accepted 30 years ago is probably not any more today.”
Animal rights charity Peta has called for the removal of equestrian events from the Olympic programme.
However, De Vos believes equestrian events – eventing, dressage, show jumping – will be at the Los Angeles Games in 2028 and Brisbane in 2032.
“I’m very confident because we’ve been doing so much for horse welfare. We will be on the programme in Los Angeles and we will also be in Brisbane,” he said.