It calls for up to six-month prison sentences for failing to register news publications with the government, and for the appointment of a new "registration official" who will be in charge of monitoring the media and issuing publishing licenses.
"This draft law is nothing but a mechanism to control the media," Kyaw Min Swe said.
"If passed in the current form, the draft law will essentially replace Burma's old censorship regime with a similarly repressive new one," said Shawn Crispin, Southeast Asia representative for the Committee to Protect Journalists. "We urge lawmakers to amend this draft in a way that protects, not restricts, press freedom."
Information Minister Aung Kyi has defended the draft bill, saying that since media censorship was abolished many new and "poisonous" publications have emerged.
He specifically referred to 46 publications that had run photographs that were "contrary to Myanmar's cultural norms," an apparent reference to scantily clad women that now appear regularly on magazine front pages. He also said there have been articles that "encouraged gambling" and others that had prompted complaints from a state-run Buddhist organization as going against Buddhist teachings.
The proposed law is "capable of decontaminating the poisoned printed matters without restricting freedom of the press," the state-run New Light of Myanmar newspaper quoted Aung Kyi as saying when he submitted the bill to Parliament on March 8.
Journalists, however, note that the proposed law could go well beyond enforcing social norms and block media from publishing material critical of the government.
The legislation would protect a constitution that among other things bars Suu Kyi from seeking the presidency in elections set for 2015. The constitution bars anyone from the presidency whose spouse, child or parent holds foreign citizenship, a clause widely criticized as being tailored for Suu Kyi because her late husband was British, and her two sons hold British nationality.
Veteran journalist Win Tin, an 83-year-old former political prisoner, said the proposed media law would inevitably lead to self-censorship.
"Journalists will be too cautious to write stories about (proposed) amendments to the constitution," Win Tin said. "It could be construed as opposing the constitution."
After the bill was submitted, the Press Council, a government-formed group made up of journalists and government appointees, issued a statement calling for the parliamentary debate to be delayed until an amended version of the law can be drafted with input from media organizations.
Aung Kyi will meet Saturday with members of the council, which is drafting a separate press law that it says will protect journalists' rights.
Associated Press Writer Jocelyn Gecker contributed to this report from Bangkok.