The BHA said that at the moment, all the affected horses were contained within the affected yard.
The horse-racing authority also said it would provide further updates on Monday evening about whether it would be possible to resume racing on Wednesday.
Last Thursday, the BHA initially cancelled all racing for the day after three cases of equine influenza were identified in vaccinated horses, but later postponed racing in Britain until the middle of this week.
The BHA also said last week that racing would not resume until Wednesday at the earliest.
The Cheltenham Festival is about a month away. The four-day event is the fourth most-attended sporting event in Britain, attracting over 260,000 visitors.
The event is also worth about 100 million pounds to the local Gloucestershire economy.
(Reporting by Gaurika Juneja; Editing by Peter Cooney)
