The Master of the National Maternity Hospital says the Eighth Amendment creates an unacceptable risk.
It is eight weeks today until polling day in the abortion referendum.
Both sides have launched their campaigns and are preparing for the debate to kick start.
Dr Rhona Mahony says some of the cases she has come across in the past made her mind up for her.
Dr Mahony said: "She was approximately 14 weeks gestation, but somatic function was maintained because she was pregnant in order to incubate her baby in what was described as a macabre experiment.
"And this was a direct consequence of the Eighth Amendment because what you had here was the conflict between, if you like, the actual clinical situation and the risk, and this balance of rights."
Meanwhile, TDs and Senators have been warned by RTÉ not to wear badges, emblems or clothing supporting either side of the abortion debate if they appear on the broadcaster talking about other issues.
In a letter sent to Oireachtas members, politicians were told they can wear items expressing a view if they are being interviewed about abortion.
However, in the interest of fair and impartial broadcasting, they should not do so if being interviewed on other subjects.
The broadcaster asked politicians to respect producers and staff if asked to remove badges or emblems before a broadcast.