The court ruled 4-3 that Mr Trump is not an eligible candidate because he had engaged in an insurrection over the US Capitol riot nearly three years ago.
The Trump campaign called the decision anti-democratic and vowed to appeal.
It is the first ever use of Section 3 of the US Constitution's 14th Amendment to disqualify a presidential candidate.
Similar attempts to kick Mr Trump off the ballot in New Hampshire, Minnesota and Michigan have failed.
Tuesday's decision - which has been placed on hold pending appeal until next month - does not apply to states outside Colorado.
The ruling only applies to the state's primary election on 5 March, when Republican voters will choose their preferred candidate for president, though it could also affect the general election in Colorado next November.
The justices wrote in their ruling: "We do not reach these conclusions lightly. We are mindful of the magnitude and weight of the questions now before us.
"We are likewise mindful of our solemn duty to apply the law, without fear or favor, and without being swayed by public reaction to the decisions that the law mandates we reach."
