A member of the public managed to gain access to Áras an Uachtaráin last Friday.
It is reported that a middle-aged woman was able to drive into the Áras grounds as maintenance work was being carried out.
She then found President Michael D Higgins and is believed to have confronted him over housing issues.
The woman was not arrested and was allowed to drive away again.
In a statement, gardaí say they do not comment on security arrangements for the President.
However, two investigations are underway, one into security measures at the Áras and a second is examining the incident itself.
The Garda statement said: "Following a recent incident at Áras an Uachtaráin, a Chief Superintendent is conducting a review of security measures and another Chief Superintendent is investigating the incident."
