Social media companies face the prospect of unlimited fines if they fail to remove posts which risk prejudicing criminal trials.
Landmark legislation to be published this week will push responsibility for online content back on to tech giants such as Google, Facebook and Twitter rather than the individual who posts it.
The use of social media has been in the spotlight since the Jobstown case earlier this year, when water protesters launched an online campaign in support of those on trial for the alleged false imprisonment of former Tánaiste Joan Burton.
Both the Supreme Court and the Law Reform Commission have previously called for contempt of court to be defined in legislation, as it is in other countries such as the UK.
The bill, written by Fine Gael TD Josepha Madigan, aims to provide clarity to judges who are struggling to deal with contempt of court issues.
Under the proposals going before the Dáil tomorrow, the courts will be able to force companies to remove or prevent the publication of prejudicial content.
It will be left to trial judges to decide the level of fine imposed if a company fails to comply.
Ms Madigan, who is also a solicitor, said she was concerned social media was not being treated in the same manner as traditional media.
"We need to protect juries from being influenced in any adverse or prejudicial way," she told the Irish Independent.
Her bill will give the law on contempt of court statutory footing for the first time. "It protects the balance between the right to free speech and the right to a fair trial," she said.
During the summer, then-chief justice Susan Denham indicated that new procedures were needed in relation to how contempt of court laws apply to posts on social media.
She said it had been rare that courts in Ireland have had to use contempt of court laws to curb inaccurate and disruptive online communications about cases. But she added: "It would be naive of us not to plan for the future in this regard."
Ms Justice Denham said the right to a fair trial didn't change "in the face of any new means of communications" and that the rules "can and must reflect the new reality".
Ms Madigan's Contempt of Court Bill 2017 gives judges the power to direct that material which risks prejudicing court proceedings be removed from websites. They would also be able to order that the website's operators take steps that the court deems "reasonably necessary" to prevent the publication of such posts. Failure to comply with such orders would be contempt of court.
The penalty for individuals found to be in contempt of court after they made posts on social media is imprisonment or a fine.
Websites could be found to be in contempt notwithstanding the fact that their administrators were not responsible for the original posting of the material.
Internet providers may be ordered to block access to the offending sections of the website, under the proposed law.
Among defences allowed for in the bill is if the website's operators can show they went "beyond what is reasonably necessary" to prevent the publication of material prejudicial to a court case.
It would not be an offence to unwittingly prejudice a trial by posting a comment on a social media site while believing a trial was not ongoing.