The court announced late Thursday it will hear arguments on that date on whether state law gives sponsors of the gay marriage ban the right to appeal a federal court decision overturning the measure.
Proposition 8, enacted by California voters in 2008, prohibits same-sex marriage by providing that "only marriage between a man and a woman is valid or recognized in California."
Last year, acting in a lawsuit filed by two couples who want to marry, U.S. District Judge Vaughn Walker of San Francisco struck down the initiative on the ground that it violated the federal Constitution.
The sponsors of the initiative and their committee, Protect Marriage, are seeking to appeal that decision before the 9th U.S. Circuit Court of Appeals in San Francisco.
Walker's decision has been stayed during the appeal, keeping the ban in effect for the time being.
But because state officials, including Gov. Jerry Brown and Attorney General Kamala Harris, have declined to appeal, the initiative sponsors have been left as the only party pursuing an appeal.
In January, a panel of the appeals court said that federal law, as defined in a 1997 Supreme Court decision, doesn't seem to allow sponsors to defend an initiative when state officials refuse to do so.
But the appeals panel said there might be a right under state law, and asked the California Supreme Court to step in and decide that issue.
The seven-member state high court will hear one hour of arguments in its State Building courtroom on Sept. 6 and then will have 90 days to issue a written ruling.
Court spokeswoman Lynn Holton said that because of public interest in the case, the court has approved a live statewide television broadcast of the arguments on the California Channel, a public affairs network.
If the state court eventually rules that the sponsors have standing, or the right to appeal, the case will then go back to the 9th Circuit for review of Walker's decision, a process that might take several more months.
But the federal appeals court said earlier this year that if the sponsors lack legal standing, the federal court would be required to dismiss the appeal.