The court handed down the ruling in the early hours of Wednesday morning, one day after a federal judge granted a stay of execution to allow for a competency hearing.
Montgomery was sentenced to death for the 2004 murder of Bobbie Jo Stinnett, a pregnant woman who was 23 years old at the time. Her lawyers have argued that she is mentally ill and cannot understand the rationale for her execution.
The death sentence is set to be carried out at a penal facility in Terre Haute, Indiana, and Montgomery will be the first female federal inmate executed since 1953.
During his presidency, Donald Trump pushed to resume federal executions after a 17-year hiatus and ten federal inmates have been put to death since June.