The high court said it would not hear a case filed by Democratic members of Congress in 2017.
A federal appeals court in Washington previously ruled that the lawsuit should be dismissed.
The appeals court did not rule on whether Trump violated the law.
It said only that the approximately 200 members of Congress who brought the lawsuit lacked the ability to sue.
As is typical when the Supreme Court declines to hear a case, the justices did not explain their reasoning.
Trump still faces other lawsuits alleging he violated the emoluments clause of the Constitution by accepting payments from foreign and domestic officials who stay at the Trump International Hotel.
In May, a federal appeals court in Virginia reinstated a lawsuit brought by the state of Maryland and the District of Columbia.
A similar lawsuit brought by by restaurant workers and a prominent restaurateur and hotelier is also ongoing.
Adapted from reporting by Associated Press.