McCain sent out runners at Ludlow and Ayr on Wednesday afternoon before vets later informed him of the news, with the trainer then contacting the British Horseracing Authority.
The origin of the infection is unclear, with McCain keen to emphasise he would never knowingly have run a potentially infected horse.
In a statement issued through the National Trainers Federation, McCain said: "I have been aware of the recent news about equine influenza outbreaks in France and Ireland, and over the last couple of days, I have been concerned about the health status of a small number of horses in the yard.
"Their welfare is at the front of our minds, so at my request, our veterinary surgeon has examined them regularly and we have followed his advice on testing and treatment.
"It was by following this protocol that the positive results for equine flu came to light yesterday evening.
"The BHA were contacted immediately and we are liaising closely with them about bio-security and management of all the horses at Bankhouse.
"Bankhouse follows all the available advice on disease control and all our horses are fully inoculated.
"We are scrupulous about observing the health status of horses in our care and taking the necessary steps to treat any condition that may affect them.
"It follows we would never race any horses that we could have known were infected.
"Over the last two months, all potential runners have been scoped and their blood checked within 36 hours of their races to ensure that only healthy horses compete for the yard.
"When new horses arrive at our yard we, as much as possible, try to keep them separate but at this stage cannot know if the infection came from recent arrivals or from horses returning from racing.
"We have three confirmed cases and this morning have taken blood and swabs from all the others for testing."
David Sykes, director of equine health and welfare at the BHA, added: "We would like to thank Donald McCain for his co-operation in this matter, and for the responsible manner in which he has dealt with this issue, under the guidance of his veterinary surgeon.
"He has acted professionally with the interests of the racing industry and the health of his horses as his priority."
