The legislation, which will come into force in January, looks set to further narrow the space for online expression in a country already branded an "enemy of the Internet" by Reporters Without Borders.
"A fine of up to USD 4,760 will be applied to anyone producing propaganda against the Socialist Republic of Vietnam," according to a copy of "decree 174" posted on a government website.
Undermining national unity, "distorting historical facts" and writing comments on Facebook that "hurt the nation" have all also become administrative offences punishable by a sliding scale of fines.
The new legislation appears to be an administrative means of punishing Facebook postings that may fall short of meeting requirements for criminal prosecution.
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Fines will be lower for individual users.
Facebook -- which has some 22 million active users in Vietnam, according to industry figures -- is the most popular social networking site in the country, despite being periodically blocked.
The government has given no clear indication of how either decree will be implemented and to date it appears no one has been prosecuted under decree 72.
Vietnam's communist government bans private media and all newspapers and television channels are state-run.
Many citizens use social media and blogs to get news and other information rather than rely on the tightly controlled official press.