During the August riots, Mr Musk shared, and later deleted, a conspiracy theory about the UK building “detainment camps” on the Falkland Islands for rioters, on X – the social media platform he owns.
At the time ministers said his comments were “totally unjustifiable” and “pretty deplorable”.
The BBC understands this is why he has not been invited to join hundreds of the world’s biggest investors at the event on 14 October.
Coming two weeks head of the Budget, the government is billing it as a huge opportunity to attract foreign investment to grow the UK economy. The Labour Party committed before the general election to hold this event within its first 100 days in office.
Under the Conservatives, Mr Musk, who owns or runs X, Tesla and SpaceX, was quietly shown around various UK sites with potential for a gigafactory for cars and batteries.
He has previously told journalists he opened a site in Germany and not the UK partly because of Brexit.
He is a regular at the equivalent French summit. In July, he attended a three-hour lunch with top executives with President Emmanuel Macron ahead of the Olympics earlier this summer.
Under his ownership of the site formerly known as Twitter, Mr Musk lifted the ban on far-right figures, including on the Britain First group.
The UK is considering a tougher Online Safety Act, after the role of misinformation in the widespread racist disorder in August.