The decision comes after the Met Office issued a 'Red' extreme heat warning, with the affected courses all falling either within the warning area or situated nearby.
Scheduled fixtures at Beverley and Windsor on Monday have been called off, as have Tuesday's all-weather cards at Chelmsford and Wolverhampton, plus Southwell's jumps fixture.
Racing in Britain is still set to take place at Ayr and Cartmel on Monday and at Musselburgh on Tuesday, with temperatures expected to be lower in Cumbria and in Scotland.
The BHA will, however, continue to monitor forecasts and any further alterations to the race programme will be announced in due course.
Richard Wayman, the BHA's chief operating officer, said: "The BHA's number one priority in the staging of any meeting is the wellbeing of all involved, human and equine. Following the issuing of the first ever extreme heat warning by the Met Office, we are taking sensible precautions and have made a decision as soon as possible in order to provide certainly for those impacted."
Mark Spincer, managing director of ARC's Racing Division and responsible for Windsor, Southwell and Wolverhampton, said: "We fully support the decision to abandon the fixtures scheduled to take place on our racecourses on Monday and Tuesday.
"We have been in close dialogue with colleagues at the BHA throughout this period of warmer weather and have been operating with a number of resources in place to assist horses and people working on our racecourses.
"Whilst we had taken steps to mitigate against the higher temperatures initially forecast for Monday and Tuesday, including moving Southwell's race times to earlier in the day, the latest updates from the Met Office and the alerts issued this morning made it clear that it was within the best interests of all concerned to abandon these fixtures.
"We will be in touch with all customers who had bookings to these race meetings shortly, and our thanks goes to the BHA team for acting swiftly in changing circumstances."
Neil Graham, director of racing at Chelmsford, said: "As ever, our primary concern is for the welfare of everyone visiting Chelmsford City Racecourse, both human and equine, and, therefore, we fully support the BHA in making this decision in such extreme conditions."
The BHA said that while the abandoned fixtures will not be rescheduled, it will review their race programmes and seek to add races in the coming days where necessary.