Lord Justice Leveson says laws are needed to prevent "mob rule" on the internet and "trial by Twitter".
The comments were his first since publishing a report on press standards in Britain last week.
Lord Justice Leveson told a privacy symposium in Sydney, Australia, that new laws would protect privacy and freedom of expression on the internet.
British newspaper editors said on Thursday they would implement his "broad proposals" for self-regulation, without new laws.
In his report into press standards and ethics last month, Lord Justice Leveson recommended an independent self-regulatory watchdog for the press, backed by legislation.
His 2000-page report contained only about a dozen pages dealing with the internet, despite saying at the start of eight months of hearings that online material was "the elephant in the room".
At a symposium entitled Privacy in the 21st Century, Lord Justice Leveson said in Sydney that the internet provided a "global megaphone for gossip" and contained an element of "mob rule".
The BBC reports he said the internet was different from mainstream media and that while the BBC had apologised for a recent Newsnight programme about child abuse, those "on the internet were not so restrained".
Lord Justice Leveson said that "there was a danger of trial by Twitter" and other forms of social media and it would "take time to civilise the internet".
He added it was likely new laws would be needed to maintain privacy and freedom of expression in the internet age.