The justices rejected the case without comment.
Lawyers for 29-year-old Brandy Holmes had argued that her mental condition, affected by fetal alcohol syndrome when she was in the womb, should prevent her execution. They say Holmes has the mentality of a 10- to 12 year-old child, CNN reported. The high court has banned the execution of the mentally retarded.
Holmes is only one of two women set for execution in Louisiana, CNN reported. She was sentenced to death for the killing of a retired minister near Shreveport, part of a crime spree in 2003.
Monday was the first day of the Supreme Court's 2009 term.