Simon Harris has asked the HSE to investigate the situation.
According to RTE, The Health Service Executive is currently investigating an apparent breach of patient information.
The situation occurred after a woman who had an abortion at the National Maternity Hospital claimed she was contacted by anti-abortion activists.
Allegedly, the woman in question got a phone call last week from a person who knew her name and was aware that she had accessed a legal abortion two days previous.
A spokesperson for the Hospital has said that it does not comment on individual cases.
"Patient confidentiality is of the utmost importance to us, and any suspected breach of confidentiality is always investigated as a matter of urgency in conjunction with other organisations who may have access to patient details."
Minister for Health, Simon Harris, said that no woman accessing an abortion should be subjected to intimidation or harassment.
A spokesperson for Mr Harris also released a statement, saying:
"The Minister has asked the HSE to investigate the alleged breach of patient information.
"The Minister has been quite clear, abortion services should be viewed as a normalised part of the health service and women accessing that service should not be subjected to intimidation or harassment."
