Sponsors of Proposition 8 and their committee, Protect Marriage, are appealing a ruling in which the 9th U.S. Circuit Court of Appeals last year struck down the initiative.
The high court's decision is expected by the end of June.
In the meantime, a stay of the lower court decision will remain in place and Proposition 8 will continue to be in effect.
The court announced Dec. 7 that it would consider the appeal, but did not specify the argument date until this week.
The court will also hear arguments on a related New York case concerning the federal Defense of Marriage Act on March 27.
The federal law, known as DOMA, bars the U.S. government from providing federal benefits and tax advantages to same-sex couples who were legally married in their state.
In the Proposition 8 case, the initiative's sponsors contend that California voters were entitled to decide to preserve the definition of marriage as the union of a man and a woman. They say that each state, working through its legislature or voters, has the right to define marriage within its territory.
Two same-sex couples who challenged Proposition 8 in a civil rights lawsuit filed in federal court in San Francisco in 2009 say the ban violates their constitutional right to equal treatment.
The court's nine justices will hear at least one hour of arguments in their Washington, D.C., courthouse beginning at 7 a.m. Pacific Standard Time.