Commentators in the US say the gathering poses numerous risks, among them, spreading Covid-19.
There are also concerns about wildfires in surrounding areas sparked by fireworks.
Trump is expected to speak at the event, and will criticise those attempting to "tear down" US history with "cancel culture".
The President will arrive in South Dakota on Friday (US time) where there will be a fireworks display at the monument.
That's despite criticism from fire chiefs of the danger posed by the displays.
Trump will then travel back to Washington DC on Saturday to view military flyovers at the National Mall and a pyrotechnics display.
The Trump administration said it would be the biggest display in living memory.
The plans in the Capitol are going ahead despite drawing objections from Washington's Mayor Muriel Bowser.
Critics say the Mount Rushmore site is symbol of Confederate oppression, having been built on land stolen from Native American tribes in violent circumstances.
The planned celebrations at Mount Rushmore have irked commentators in the US, after Trump's political supporters said the event will go on without social distancing.
The Republican Governor of South Dakota Kirsti Noem said face masks would be available at the event but said "we won't be social distancing".
"We told those folks that have concerns that they can stay home," she said.
Some 7500 people are expected to attend the event.
Activist groups have long taken issue with Mount Rushmore monument which was formerly known as the Black Hills area.
The area was given to the Lakota Siuox in a treaty but then taken from them by force in the 1870s.
Two of the four faces carved into Mount Rushmore — George Washington and Thomas Jefferson — were also slave owners.
It's expected Trump will speak about protesters who he claims are trying to "tear down" the US, according to a Trump campaign official.
"The left wing mob and those practising cancel culture are engaging in totalitarian behaviour that is completely alien to American life – and we must not accept it," the official told the BBC, in a summary of the expected comments from the President.
It comes after the President spent recent days tweeting about monuments and statues being torn down across the US.
