The Immigrant Council of Ireland says the racist abuse towards former England footballer Ian Wright happens regularly online.
An 18-year-old man from Co Kerry has been interviewed about the incident.
On Monday afternoon, Mr Wright - a former Arsenal and England striker - highlighted the abuse he had received on social media.
He said he knows he is "not meant to look at them" but that the messages "hit me so hard".
In a reply to a message of support, he said: "I'll always love the Irish... We'll always be inextricably linked my brother. No Blacks, No Irish, No dogs! Lest we forget".
The Irish Network Against Racism (INAR) has said in the first quarter of this year, racist incidents in this country doubled.
Shane O'Curry, a director of the organisation, said there has been a huge increase in online abuse since the lockdown.
He also hit out at the Ian Wright incident.
"The first thing that struck me were two things: one [was] the dignity of his response towards Irish people on Twitter.
"He was very careful not to tar all Irish with the blame for this.
"But on the other hand it was very clear from his response that this was one that he could not ignore.
"The vehement of this was so strong that it had clearly impacted on him.
"He said that he couldn't ignore this one and let it go away".
Pippa Woolnough, from the Immigrant Council of Ireland, says this type of abuse is not rare online.
"It's more common than we would like to realise, and that's why it's so important that we talk about it and that we talk about the alternatives.
"And that we realise that we're educating our young people, that things that are said online are just the same as things that you say outloud: and they do affect people, that do cause hurt and anguish and it's just not acceptable in our society".
An 18-year-old man from Co Kerry has been interviewed about the incident, after he presented himself to a Garda station.
A file is being prepared for the Director of Public Prosecutions (DPP).
Gardaí say while no formal complaint has been received, an investigation is underway into the comments in line with its Diversity and Integration Strategy.
They are appealing to the public not to engage in social media commentary in relation to this matter.
London's Metropolitan Police have also reached out to Mr Wright in relation to the incident.
Additional reporting: Eoghan Murphy