Senior staff in the Department of Health were quarantined for hours after an envelope containing white powder was sent to Health Minister Simon Harris yesterday.
The entire department was evacuated after the alarm was raised shortly before noon when a staff member in the minister's private office opened the envelope.
The substance was later found to be baking powder.
Taoiseach Leo Varadkar said last night he did not know what type of "oddballs" would send suspicious packages to politicians, but added that post would never be opened by a public representative, always by staff.
"If you want to come after us, come after us - but don't come after our staff or our families," he said.
No note or threat was att-ached to the package, and a full garda investigation is under way.
A source close to the minister said last night that his immediate concern following receipt of the envelope was for his staff - including a new member of the team - who were directly affected by the worrying incident.
"He was upset for the people involved," the source said.
Around a dozen senior staff in the minister's private office were quarantined until specialists had declared the substance harmless.
The minister did not come into contact with the powder and was ushered out along with the rest of the staff in Miesian Plaza on Baggot Street, which is also home to the Department of Children and Youth Affairs.
In a brief statement on Twitter last night, the minister thanked emergency services for their response.
"Thank you to the emergency services for their diligence today in responding to an incident at my department," he said.
"The safety of staff must always be paramount. Today was a difficult day for them all and particularly those who work so closely with me in my office."
Children's Minister Katherine Zappone, who was also ushered from the building, expressed concern for staff who opened mail.
"I did see Minister Harris as well afterwards. We were both over in Leinster House continuing our meetings having evacuated and I just said to him, 'Simon, you know I'm so sorry this has happened to you'," she said.
"It's just completely unacceptable. This is after a number of other targets in relation to, in my view, the leadership and efforts that he is offering in terms of his ministry and it is very, very worrying from that perspective, too."
The Independent minister went on to say "it should not be happening, but above all I want to say that really the people who are most unsafe in this regard are staff, and that's completely unacceptable".
A motion of no-confidence in Mr Harris was recently tabled by Sinn Fein in response to controversy over the massive cost escalation relating to the National Children's Hospital.
Gardai and members of the Army Bomb Disposal Team were dispatched to the scene when the alarm was raised yesterday and a significant security presence rolled out.
The area was cordoned off and specialist technicians were deployed to examine the substance.
Staff were sent home, and the scene was declared safe at 2.30pm.
While there is no suggestion that the alert yesterday is linked to earlier events, it is the latest in a series of incidents that have led to a review of ministerial security arrangements.
A number of weeks ago Mr Harris was targeted by protesters at his Wicklow home.
The minister believes the group followed his wife and baby home from a walk on a Sunday afternoon.
Richard Bruton has also been targeted by the group, while protesters have gathered near the home of the Taoiseach in recent weeks.
Ahead of those protests gardai were also investigating a threat to "evict" female ministers from their homes.