The meetings scheduled for Hamilton, Leicester, Warwick and Wolverhampton will be cancelled as a mark of respect.
The Queen, who died at the age of 96 on Thursday, will lie in state "four clear days" in Westminster Hall, arriving there on Wednesday September 14 until 6.30am on the morning of her funeral, a senior palace official said.
Thousands of people will be able to file past to see the late monarch's coffin - and further details of how the public can attend will be announced in the coming days.
No racing took place in Britain on Friday and Saturday. It will resume with a nine-race card at Doncaster - which will include the final Classic of the season, the Cazoo St Leger - on Sunday.
A statement from the British Horseracing Authority said that racing will not take place on the day of the the Queen's funeral on Monday week, however.
"British racing will not go ahead on Monday September 19 for the funeral of Her Late Majesty The Queen," the statement read.
"This will give everyone involved in British racing the opportunity to mourn Her Late Majesty's passing and offer thanks for her contribution to our sport and the nation.
"The fixtures on Monday September 19 will therefore be cancelled. Further information will be shared with participants, racecourses and racegoers in the coming days.
"Racing will take place as scheduled throughout the remainder of the intervening period."
On Monday, the Queen's coffin will be taken from Holyroodhouse in procession to St Giles's Cathedral where it will lie at rest until Tuesday September 13, before being taken by air by RAF plane to London, where she will lie in state.
A spokesman for King Charles III said the monarch's main focus will be leading the royal family and nation in mourning over the coming days.
"Whilst, in the next few days, the King will carry out all the necessary state duties, his main focus will be leading the Royal Family, the nation, the Realms and the Commonwealth in mourning Her Majesty The Queen. This will include meeting members of the public, to share in their grief," the spokesman said.