President Julian Bear Runner cited health fears over the coronavirus and also said that Mr Trump's attendance is an insult to Native Americans on whose stolen land it was built.
“Trump coming here is a safety concern not just for my people inside and outside the reservation, but for people in the Great Plains. We have such limited resources in Black Hills, and we’re already seeing infections rising,” Mr Bear Runner said in an interview with The Guardian.
Several Native American groups are planning to stage protests over the president's scheduled appearance, the newspaper reported.
“It’s going to cause an uproar if he comes here. People are going to want to exercise their first amendment rights to protest and we do not want to see anyone get hurt or the lands be destroyed,” Mr Bear Runner added.
The fireworks event is set to go ahead at the monument on Friday evening as part of the state's Independence Day celebrations and is expected to be attended by around 7,500 participants despite the ongoing coronavirus pandemic.
Governor Kristi Noem confirmed that attendees will not be required to practise social distancing or wear masks during the event.
The Sioux president said that the visit would violate historic treaties between the US government and Native Americans that permit them sovereignty over the sacred Black Hills that the site is carved into.
“The lands on which that mountain is carved and the lands he’s about to visit belong to the Great Sioux nation under a treaty signed in 1851 and the Fort Laramie Treaty of 1868 and I have to tell him he doesn’t have permission from its original sovereign owners to enter the territory at this time,” Mr Bear Runner said.
The US Supreme Court ruled in 1980 that the Black Hills, over which they held sovereignty in perpetuity under the 1868 treaty, had been seized from the Sioux illegally by the federal government after miners seeking gold in the area forced them to release the land.
Mr Bear Runner added that Mr Trump should have asked permission for the trip from the seven Sioux tribal governments before planning to make the visit.
“As leader of the United States he has obligation to … honour the treaties that are the supreme law of the land,” the 34-year-old told the newspaper.
Native American activists have argued for years that the memorial to four US presidents, George Washington, Thomas Jefferson, Abraham Lincoln and Theodore Roosevelt – which was completed in 1941 – should be removed due to being built on stolen lands and the figures' links to slavery and racial oppression.
“The rocks already had spiritual meaning before westerners came to squat on our territory,” Mr Bear Runner said. “The land is rightfully ours, and we didn’t give the Black Hills over. It would be wrong for me as a tribal leader to remain diplomatic. We consider the carvings a symbol of trying to wipe us away and to say they had conquered us."
The monument was designed and executed by Gutzon Borglum, an American sculptor and artist who himself had ties to white supremacy.
Lincoln in particular functions as a symbol of offence to Native Americans as he ordered the hanging of 38 Sioux in Minnesota during the Dakota war of 1862.
“They don’t tell the true story and it’s wrong. We hear only the highlighted story of the good things these men have done for this country but they don’t tell that this land belongs to Native Americans, that the Black Hills belong to the Sioux nations, or the hanging of these Dakota men,” Mr Bear Runner said.