Lawmakers say it will protect Burundi leaders and citizens but local media call it an attack on press freedom in a central African nation recovering from more than a decade of civil war.
Although the media operate with some freedom in landlocked Burundi, several journalists have been jailed and independent outlets threatened with closure in the last few years.
New York-based Human Rights Watch said last year the government was trying to restrict efforts by independent media and civil society to criticise violence blamed on the state.
Under the bill passed by the national assembly late on Wednesday, journalists, newspapers or radio businesses will be liable to pay fines from $2,000 and $6,000 for press offences.
It also bans the media from publishing news about national defence, public safety, state security and the local currency, which lost 14.3 percent against the dollar in 2012 and is down 4 percent in 2013.
"This bill was approved by the majority of members of parliament, because we believe it guarantees the freedom of expression for journalists, but it also protects the rights of citizens and country's leaders," said Pie Ntavyohanyuma, speaker of the national assembly.
Burundi's journalists union (UBJ) said the bill was an unconstitutional attack on press freedom.
"This bill denies the freedom of expression and media, it is against the country's constitution and other international laws such as the universal declaration of human rights," said Alexandre Niyungeko, the UBJ chairman.
The bill has to be approved by the senate before President Pierre Nkurunziza can sign it into law. (Reporting By Patrick Nduwimana; Editing by Drazen Jorgic and Alistair Lyon)