The court's one-page order, issued without comment, lets stand a federal appeals court decision that allowed the week to be eliminated.
"Golden Week" was adopted after the 2004 election when some voters were forced to wait up to 12 hours to vote. It was part of an overhaul of the state electoral system. But in 2013, Republicans moved to cut back early voting from 35 days to 28 days.
Democrats charge that Republicans pushed for the new law because a disproportionate numbers of African Americans, who were exerting a growing political influence in the state in support of President Barack Obama, had come to rely upon more early vote opportunities.
In court papers, Marc Elias, a lawyer for the Ohio Democrats, said that "Golden Week has formed an essential part of the election reforms that ameliorated, but did not completely remedy, the long lines, chaos and confusion that plagued the 2004 presidential election in Ohio."
Elias, who also serves as general counsel for the Clinton campaign, argued, "Tens of thousands of Ohio voters have relied on Golden Week during the past two presidential elections, and African-Americans have done so at far higher rather than other voters."
Lawyers for Ohio had urged the court to leave the lower court opinion undisturbed. They argued that even without Golden Week the state had generous early vote opportunities compared to most other states.
"Ohio remains a "national leader when it comes to early voting opportunities
," the state's Attorney General Mike DeWine argued in court papers.
Earlier this year, a federal district judge said the state must reinstate Golden Week. A federal appeals court reversed that last month, in part citing the options Ohio gives for early voting.
"The issue is not whether some voter somewhere would benefit from six additional days of early voting or from the opportunity to register and vote at the same time," Judge David McKeague of the United States Court of Appeals for the Sixth Circuit, wrote in the opinion. "Rather, the issue is whether the challenged law results in a cognizable injury under the Constitution or the Voting Rights Act. We conclude that it does not."
The law afforded "abundant and convenient opportunities for all Ohioans to exercise their right to vote," the court added.
Judge Jane Branstetter Stranch, writing in dissent, said she agreed with the district's court finding in May that the law "improperly burdens the right to vote of African-American citizens of Ohio and constitutes a violation equal protection."
McKeague and Judge Richard Allen Griffin were appointed by President George W. Bush, while Stanch is a nominee of Obama.