Dujardin did not elaborate on the investigation but revealed the International Federation for Equestrian Sports (FEI) were looking into an old video where she admitted to making an "error of judgement" and apologised.
"A video has emerged from four years ago which shows me making an error of judgement during a coaching session," she said in a statement.
"Understandably, the International Federation for Equestrian Sports (FEI) 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."
Dujardin said she was "sincerely sorry" for her actions and was 'devastated' on letting down the team, 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."
Dujardin won three golds, a silver and two bronze medals at the London, Rio and Tokyo Games.
With six medals, she is Britain's joint-most decorated female Olympian alongside cyclist Laura Kenny.
'Genuine remorse'
Dujardin won three golds, a silver and two bronze medals at the London, Rio and Tokyo Games in individual and team dressage.
With six medals, she is Britain's joint-most decorated female Olympian alongside cyclist Laura Kenny.
"We are deeply disappointed with this case, especially as we approach the Olympic Games in Paris 2024. However, it is our responsibility and crucial that we address any instances of abuse, as equine welfare cannot be compromised," FEI president Ingmar De Vos said.
"Charlotte has expressed genuine remorse for her actions, and we recognise and appreciate her willingness to take responsibility.
"Despite the unfortunate timing, we believe this action reaffirms the FEI's commitment to welfare as the guardians of our equine partners and the integrity of our sport."
Dujardin, ranked fourth in the FEI world dressage standings, was set to ride 11-year-old gelding Imhotep in Paris. She won team gold in the European Championships in September last year.
Becky Moody riding Jagerbomb is the alternate for the British team. The equestrian events at the Paris Olympics begin on Saturday.
