Google, Facebook and Twitter could face fines of up to €20 million for failing to remove harmful or abusive content.
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.
