The federal government, continuing its string of executions this year, has set the dates for two more, including the first woman in more than six decades.
Montgomery strangled and killed Bobbie Jo Stinnett, who was 8 months pregnant, in 2004.
The last woman executed by the US government was Bonnie Brown Heady on December 18, 1953, according to US Bureau of Prisons records, for kidnapping and murder.
Montgomery, who was found guilty of strangling a pregnant woman in Missouri, will be executed by lethal injection at US Penitentiary Terre Haute, Indiana, the department said in a statement.
The Trump administration resumed executions of federal inmates earlier this summer for the first time in almost two decades.
Montgomery drove from her Kansas home to Stinnett's house in Skidmore under the guise of adopting a rat terrier puppy, prosecutors said.
She was put to death in a gas chamber in 1953. At the time, Montgomery's lawyers had argued that she was suffering from delusions when she killed Stinnett, but the jury rejected the defense.
The Justice Department also scheduled Brandon Bernard, a 40-year-old man found guilty in the 1999 killing of two youth ministers in Texas.
Kelley Henry said Montgomery, her client, is mentally ill, suffered terrible childhood abuse, and had poor representation at trial. "But her severe mental illness and the devastating impacts of her childhood trauma make executing her a profound injustice", Henry claimed.
This came after the White House announced past year that the Bureau of Prisons was switching to a new single-drug protocol for lethal injections, from a three-drug combination that the bureau last used in March 2003 on a former soldier convicted of rape and murder.
Bernard and his co-defendant, Christopher Vialva, were convicted in the 1999 kidnapping and killing of Todd and Stacie Bagley, an Iowa couple who had stopped to use a payphone in Killeen, Texas.
Vialva was executed last month at the Federal Correctional Complex in Terre Haute.
The Trump administration ended an informal 17-year-hiatus in federal executions in July, after announcing last year that the Bureau of Prisons was switching to a new single-drug protocol for lethal injections, from a three-drug combination it last used in 2003. Anti-death penalty groups say US President Donald Trump is pushing for executions during the campaign season in a bid to burnish a reputation a law-and-order leader.