President Rachel Walker said the matter was being managed by the North Otago A&P Show's leadership but she had shared the executive's serious concerns regarding the situation and offered their support.
She was aware of social media commentary around the incident and said it was important that people allowed the resolution process to play out.
"While we appreciate the distress and serious concern being shared by many, we don't support any personal or pointed attacks that may cause harm — whether physical or otherwise — to the woman in the video."
SPCA national inspectorate manager Alan Wilson said the animal welfare organisation was ready to assist MPI with any investigation should it be called upon.
"SPCA was shocked by the behaviour displayed in this video, and on the face of it this may be a breach of the Animal Welfare Act," Wilson said.
The incident came only weeks after New Zealand Olympic equestrian champion Sir Mark Todd received international condemnation when a video emerged showing him striking a horse with a branch.
WATCH: Event rider Sir Mark Todd apologises after repeatedly whipping horse with stick
SAFE spokesman Will Appelbe said whether someone was "world-famous or an unknown", there was no excuse for beating an animal.
Appelbe said the actions of the rider in Oamaru were disgraceful and called on the authorities to "immediately" investigate the incident and take appropriate action.
"After the swift condemnation of Mark Todd's treatment of a horse recently, these horse riders should know better.
"It's completely unacceptable to treat horses like this. We're seriously concerned that this behaviour could be more widespread."
Multiple attempts to contact the rider have been unsuccessful.
