Hill Sixteen was the third horse to die at this year's three-day festival after a heavy fall at the first fence of Saturday's National.
Dark Raven was put down after falling in the Mersey Novices' Hurdle earlier on Saturday and Envoye Special died after a fall in the Foxhunters' Chase on Thursday.
Two other horses, Recite A Prayer and Cape Gentleman, were assessed by veterinary staff on the course.
"Our thoughts are with everyone connected to the horses who suffered fatal injuries this week," Julie Harrington, the Chief Executive Officer of the BHA, said in a statement.
"No one will be more affected by this news than the trainers, owners and stable staff who have provided these horses with first-class care and attention throughout their lives.
"The BHA and Aintree racecourse will now analyse the races in painstaking detail, as is the case every year, to build on our existing data and help us understand what caused these incidents."
The start of the National, one of the highest-profile events in Britain's sporting calendar, was delayed for around 15 minutes after the protesters made their way on to the course.
The protesters say the race is cruel to horses, with many having died over the daunting fences down the years.
Merseyside Police said 118 arrests had been made on suspicion of offences including criminal damage and public nuisance after protesters scaled perimeter fencing and tried to attach themselves to fences before they were dragged away.
"We respect the right of anyone to hold views about our sport but we robustly condemn the reckless and potentially harmful actions of a handful of people in disrupting the race at a time when horses were in the parade ring," Harrington added.
"The Grand National is and always will be an iconic sporting event and the actions of a small number of people will do nothing to diminish its huge and enduring international appeal."
