Lib Dem MP John Hemming has used parliamentary privilege to name Ryan Giggs as the married footballer named on Twitter as having an injunction over an alleged affair with a reality TV star.
During debate in the Commons on 23 May 2011, Mr Hemming said it would not be practical to imprison the 75,000 Twitter users who had named the player.
Earlier the High Court again ruled that the injunction should not be lifted.
Following an urgent question from Tory MP and culture committee chairman John Whittingdale, Attorney General Dominic Grieve announced that a joint committee of peers and MPs would investigate the use of court injunctions to protect privacy.
He said it would examine whether the current system was working following recent controversy over super-injunctions.
Mr Grieve refused to be drawn on any individual cases following Mr Hemming's comments.
But Mr Whittingdale said the use of social media such as Twitter to breach injunctions was in danger of making "the law look an ass".
He told Mr Grieve: "You would virtually have to be living in an igloo not to know the identity of at least one Premier League footballer who has obtained an injunction."
Mr Grieve warned: "The courts do have power to punish those who breach injunctions and those who decide flagrantly to do so should bear that in mind when they embark on that course of action."