Dujardin, a three-time Olympic champion, said in a statement she had withdrawn from all competition while the International Federation for Equestrian Sports (FEI) investigates the incident.
It was not immediately clear what the video showed.
"What happened was completely out of character and does not reflect how I train my horses or coach my pupils, however, there is no excuse," she said.
"I am deeply ashamed and should have set a better example in that moment."
Dujardin, 39, could have become Britain's most decorated female Olympian in Paris. A medal of any colour would have taken her clear of Laura Kenny, with whom she is currently tied on six medals.
"A video has emerged from four years ago which shows me making an error of judgement during a coaching session," she said in the statement.
"Understandably, the International Federation for Equestrian Sports is investigating and I have made the decision to withdraw from all competition - including the Paris Olympics - while this process takes place.
"What happened was completely out of character and does not reflect how I train my horses or coach my pupils, however there is no excuse. I am deeply ashamed and should have set a better example in that moment.
"I am sincerely sorry for my actions and devastated that I have let everyone down, including Team GB, fans and sponsors.
"I will cooperate fully with the FEI, British Equestrian Federation and British Dressage during their investigations, and will not be commenting further until the process is complete."
