The law was adopted by the government during the night, the official SANA news agency reported.
The government "adopted a draft law regarding political parties in Syria as part of a programme of reform aimed at enriching the political life, creating a new dynamic and allowing for a change in political power," SANA said.
Multipartism is a core demand of anti-regime protesters who since March 15 have been taking to the streets across Syria almost daily to call for political freedoms and an end to the authoritarian rule of President Bashar al-Assad.
"The bill stipulates the essential objectives and principles governing the activities of parties, conditions for their establishment ... and rules relating to their financing, their rights and their obligations," SANA said.
It prohibits parties founded on the basis "of religion, tribal affiliation, regions and professional organisations as well as those which discriminate on the basis of race, sex or colour," the report said.
It added that non-Syrian parties are also banned. The Baath party has been in power since 1963. According to the constitution it "leads society and state."