That would be the maximum fine under new legislation being prepared by the Minister for Arts and Media Catherine Martin.
Ms Martin told the Sunday Times the material could relate to the likes of child sex abuse, terrorism, cyber-bullying and eating disorders.
A new Media Commission will be set up that can hand out fines to social media sites, search engines or messaging apps that do not comply with repeated requests to take down content.
Ms Martin referenced abuse received by her fellow Green Party member, Lord Mayor of Dublin, Hazel Chu, which the Minister described as "appalling racism" on Twitter.
Ms Chu appeared on Friday night's Late Late Show, detailing some of the abuse she has been subjected to online.
Hear Hear. So proud of our @greenparty_ie colleague and friend @hazechu . Still has a smile on her face despite all the appalling racism she has faced. Strong, courageous and inspirational as always https://t.co/gSn914gqTr
— Catherine Martin TD (@cathmartingreen) September 19, 2020
Ms Martin added that state funding for Arts events may be linked to organisers having clear procedures in place for dealing with sexual harassment, saying she was concerned for teenagers attending festivals.
This follows a number of posts in the Mise Fosta social media campaign, in which women share stories of sexual assault in the traditional music scene.
