Lisa Montgomery was convicted of killing 23-year-old Bobbie Jo Stinnett in the northwest Missouri town of Skidmore in 2004.
She used a rope to strangle Stinnett, who was eight months pregnant, and then cut the baby girl from the womb with a kitchen knife.
Montgomery took the child with her and attempted to pass the girl off as her own.
Her execution comes as another court halted two other executions set for later this week because the inmates tested positive for Covid-19.
The three executions were to be the last before President-elect Joe Biden, an opponent of the federal death penalty, is sworn-in next week.
Montgomery's lawyers have long argued she is mentally ill and cannot comprehend she would be put to death.
Separately, a federal judge for the US District of Columbia halted the scheduled executions later this week of Corey Johnson and Dustin Higgs in a ruling on Tuesday.
Johnson, convicted of killing seven people related to his drug trafficking in Virginia, and Higgs, convicted of ordering the murders of three women in Maryland, both tested positive for Covid-19 last month.
One of Montgomery's lawyers, Kelley Henry, told The Associated Press on Tuesday morning that her client arrived at the Terre Haute facility late Monday night from a Texas prison and that, because there are no facilities for female inmates, she was being kept in a cell in the execution-
chamber building itself.
"I don't believe she has any rational comprehension of what's going on at all," Ms Henry said.