The relatives of employees at the south Dublin hospital were vaccinated with doses left over from a batch.
Stephen Donnelly said he will speak with the chairman of the Coombe Hospital board about the matter.
Trust in the vaccine programme is of critical importance and what happened should not have happened
Health Minister Stephen Donnelly
A spokeswoman for the hospital said 16 doses of the vaccine were left after 1,100 frontline workers, including GPs and community health staff, were vaccinated.
The hospital said that, of the 16 recipients, nine were over 70 and the other seven were of varying ages.
The hospital said the doses would have been thrown out if they had not been administered.
In a statement issued on Monday morning, Mr Donnelly said he found out about it on Sunday night.
He said: “I was made aware on Sunday night of a situation with regard to the administration of vaccines on Friday January 8, at the Coombe Women and Infants University Hospital in Dublin.
“Trust in the vaccine programme is of critical importance and what happened should not have happened.
“Our vaccine allocation strategy clearly sets out a priority list for vaccination – and that’s currently for frontline healthcare workers and residents and staff of our long-term residential care facilities.
“It does not include family members of healthcare workers.
“I will be speaking with the chair of the Coombe Hospital Board for a full account.”
The master of the Coombe hospital, Professor Michael O’Connell, said the decision was made to ensure that not a “single reconstituted vaccine was wasted”.
He added: “Had they not been used, they would have been discarded.
“I was keenly aware of that and, throughout the evening and from 9.30pm onward, I personally made every effort to prioritise and identify additional frontline workers and followed all measures available to me at the time.
“In hindsight, as master, I deeply regret that family members of employees were vaccinated and for that I wholeheartedly apologise.”
It came as some 1,800 GPs, practice nurses and other healthcare staff received Moderna jabs at mass vaccination centres in Dublin, Galway and Portlaoise.
On Monday, the number of coronavirus patients in hospital continued to surge, with 2,032 now in hospitals across Ireland.
HSE director-general Paul Reid said critical care surge plans have been activated.
He tweeted: “2,023 patients are now in hospital with Covid-19.
“Over 400 are receiving high grade ventilation and respiratory support inside and outside of ICU.
“Our national critical care surge plans are activated.
“We’re working really hard to remain in control. Your help counts.”
Hundreds of people have been slapped with fines amounting to thousands of euros for travelling more than 5km from their home for non-essential reasons over the weekend.
Gardai in Wicklow said they issued more than 100 fixed payment notices at 100 euro each, and turned away some 200 drivers after issuing them with a caution.
Officers were targeting people travelling to the Wicklow mountains, after hundreds of cars caused traffic issues in the area in recent weeks.
The number of people receiving the Pandemic Unemployment Payment (Pup) has jumped by more than 61,700 in the last week, figures show.
Almost 469,000 people are now in receipt of the weekly Pup, amounting to a total of 138.07 million euro.
The Department of Social Protection said the sector with the highest number of people receiving Pup is accommodation and food service, followed by wholesale and the retail trade, and construction.
The construction sector has seen the largest increase, with 56,217 people receiving a Pup.
This increased from 32,152 recipients last week, which is attributed to the Level 5 restrictions imposed on the sector on Friday January 9.