The new law, dubbed Decree 72, limits what Vietnamese citizens can post on their online personal pages, including Facebook, Twitter and blogs.
Decree 72 does not elaborate on what constitutes a breach.
The law also demands all foreign websites maintain at least one server in Vietnam, which would give the government greater control of content.
Media freedom watchdog Reporters Without Borders criticized the decree before it became law, calling it "the harshest offensive against freedom of information" in the country since its prime minister signed a tough round of sanctions against media in 2011.
The organization urged nations to impose heavy sanctions against Vietnam if the country allowed the decree to become law.
Vietnam has been criticized by the United States and leading internet firms like Google and Yahoo! over the controversial internet decree, which it said had been misunderstood and did not breach human rights.
Reporters Without Borders has previously labelled Vietnam an enemy of the internet and ranks the nation 172 out of 179 in its press freedom index. Vietnam jails the second most bloggers and cyber-dissidents, according to the organization — with 35 people currently imprisoned.