Outlining the consultation online, the independent body set up to keep the law under review and recommend reforms, said new media platforms "pose a number of challenges" and therefore the law needs to be reviewed.
As described by the commission, the law "covers a wide variety of conduct which undermines or has the potential to undermine the course of justice, and the procedures which are designed to deal with them".
In the consultation paper, concerns were said to have been raised about "the impact of new technology on the question of who constitutes a publisher for the purposes of the Act".
"As more than one stakeholder commented, the rise of social media and so-called citizen journalism means that 'everyone is a publisher' now," the report adds.
"We examine how the substantive and procedural aspects of the law may need to be reformed to meet these developments."
One proposal from the commission, made in the paper, is that "courts be provided with a power to make an order when proceedings are active, to remove temporarily a publication that was first published before proceedings became active, which creates a substantial risk that the course of justice in the proceedings in question will be seriously impeded or prejudiced".
The consultation follows a number of recent contempt proceedings, including "the first internet contempt by publication, which concerned the posting of an incriminating photograph of a defendant on a website" and "contempt proceedings for the vilification of Chris Jefferies during the investigation into the murder of Joanna Yeates".
A specific area of the consultation addresses "the new media", in light of the current contempt laws "pre-date the internet age".
"In addition, there are concerns that some aspects of the law or procedure relating to contempt of court may be unclear or incompatible with the European Convention on Human Rights," the commission adds.
"The consultation considers whether the law and procedure for dealing with the contempts outlined above are adequate.
"It proposes a number of reforms, which are intended to make the law fair, understandable, practicable and 'future-proof'."
The consultation will close on 28 February 2013.