"The restrictions we are putting in place to close racing to spectators and limit attendees will reduce demand on public services. We also have a range of measures in place designed in response to the government's guidance on public health and we will continue to update these as appropriate."
Contrary to many European countries battling the crisis, Britain is yet to ban mass gatherings, but the Premier League and Football League have opted to suspend soccer matches.
Continuing with horse racing will be some comfort for the British betting industry which has been denied much of the live sport on which its business is based.
The BHA said, however, that the situation is fluid and "decisions may have to be made to cancel meetings".
"Every effort will be made to notify customers and the betting industry at the earliest opportunity," it said.
Britain recorded another 171 cases of coronavirus on Monday, taking the total to 1,543. (Reporting by Martyn Herman, editing by Ed Osmond)