Gardaí are urging the public to report any incidents of people coughing or spitting at them, saying they will treat such cases “seriously”.
Garda HQ has warned those involved in such behaviour that they could face prosecution and a criminal record.
The Association of Garda Sergeants and Inspectors (AGSI), representing frontline supervisors, described the actions as “disgraceful” and said they “will not be tolerated”.
The comments come on the back of a number of such incidents, including one involving a youth coughing at a garda in Co Waterford and remarks from Health Minister Simon Harris that he was coughed at by a couple.
There have also been various social media reports of similar incidents, some involving groups of teenage boys surrounding or closely passing people.
In a statement, Garda HQ said it was “aware of ongoing social media” reports in relation to people engaged in coughing at individuals.
“Any member of the public should report such activity to An Garda Síochána and not on social media,” the statement said.
“This activity could amount to an offence under the Public Order Act or Non-Fatal Offences Against the Person Act. An Garda Síochána will treat any reports of this type of activity seriously.”
It confirmed that a teenage male was arrested for a public order offence in Dungarvan, Co Waterford, on Monday and that an investigation was underway.
The arrest occurred after gardaí tried to break up a kick-about involving 10 people on a green, but the youth verbally gave out to a garda, then allegedly coughed in his direction.
AGSI deputy general secretary Antoinette Cunningham said: “It is disgraceful that such actions are taken by members of the public. We do not condone such behaviour and it should not and will not be tolerated.
"At a time when the country is going through an intensely difficult period, we need to work together. We appeal to the public to report any such incidents and also to follow public health guidelines at all times.”
Minister Harris warned against people playing "games" over the Covid-19 virus after a man and woman randomly ran up to him on the street and coughed at him.
“This happened to me yesterday as I was walking from here to my department and a man and woman on the street thought it was hilariously funny to come up cough at me and run-off laughing”.
Mr Harris warned people about engaging in such irresponsible behaviour, given the large numbers of deaths from the spread of the virus in other countries.
"Can we please as people just look at what's happened in Italy, in the European Union, where we're seeing several hundred people a day dying of the virus that can be deadly to certain people in our population.
“When you think, I think particularly older people who are being targeted in relation to this, there seems to be some sort of social media, a game, but it is not a game, it is disgusting, that you will target certain people in your community, generally older people, and go up and cough in their face and video it and have a laugh and run off.
The Lord Mayor of Cork, Dr John Sheehan, a GP, said instances of coughing or groups drinking outside proved that more targeted public health messaging was required.
"Convincing young people, especially, to take this seriously remains a challenge," he said.
"A lot of them just don't get public health messages. When you're young, you feel invincible, as if nothing will happen to you. And there is always that sense of rebellion against authority."
Fianna Fáil TD for Kildare North James Lawless said he had heard of reports of people taking part in the “corona challenge” by deliberately coughing into the faces of people and uploading it on social media.