In a unanimous decision, the justices said that the four Republicans were not entitled to sue in an effort to replace a redistricting plan ordered by a court with one passed by a Republican-controlled state legislature.
A Democratic state judge drew up the first redistricting plan in 2002, while the Republican Legislature drew one up in 2003.
The court plan had been put in place when a divided Colorado General Assembly was unable to agree on one in time for the 2002 election.
In their lawsuit, the Republican voters say the court-imposed map violates a right of citizens under the U.S. Constitution to vote for congressional candidates in districts created by state legislatures.
In an unsigned opinion, the justices said that the only injury the Republican voters allege is that the Elections Clause had not been followed.
"This injury is precisely the kind of undifferentiated, generalized grievance about the conduct of government that we have refused to countenance in the past," the court stated.
Citing earlier rulings, the justices said the Republicans must have more than a general interest common to all members of the public in order to pursue the case.
Last year, a U.S. District Court in Colorado had ruled that the Republicans could proceed with their lawsuit asserting an Elections Clause violation.
The Colorado case is the Supreme Court's latest foray into congressional redistricting battles. Last year, the justices addressed a messy redistricting fight in Texas, ruling that the Constitution does not bar states from redrawing political lines in mid-decade when one party or the other senses an advantage.
The decision grew out of a court review of a Texas redistricting plan orchestrated in 2003 by Tom DeLay, who was a Republican congressional leader at the time.
The Colorado dispute also involved a lawsuit brought by the Democratic state attorney general. It led to a Colorado Supreme Court decision against the Republican legislative plan in 2003. The Colorado Supreme Court said the state constitution restricts congressional redistricting to once per decade and that the legislature's plan was the second plan.