A Fianna Fail MEP attended the election of new Taoiseach Micheal Martin the day after arriving in Ireland from Brussels.
Bill Kelleher apologised unreservedly after failing to self-isolate.
He said the health risk from the virus could not have been eliminated fully and he should have remained at home.
Anyone arriving in Ireland from abroad is asked to self-isolate for 14 days, the HSE said.
Mr Kelleher said: “Last Saturday, I attended the election of the new Taoiseach in Dublin having arrived into Ireland from Brussels the day before.
“As I previously stated, I avail of Covid 19 testing services before in advance of departing Brussels in order to reduce any potential public health risk.
“However, despite this, I accept that the risk could not have been eliminated fully and I should have followed HSE advice and remained at home.
“This was an error of judgment on my part and I apologise unreservedly.”