The proposed law, which is valid for 18 months, is described by Chavez' allies as a key step in their self-styled socialist revolution.
"We welcome this enabling law, with the support of the National Assembly, which backs our leader," Cilia Flores, the legislative president, said after a unanimous how of hands in favour during the four-hour session.
But Flores said: "There will always be opponents, and especially when they know that these laws will deepen the revolution."
Chavez, in power since 1999, began serving a new term a week ago after a conclusive election victory in December.
Among the new measure he is expected to introduce if the special law is passed are the abolition of the independence of the central bank and the nationalisation of Venezuela's telecommunications and electrical industries.
He has already announced Venezuela will acquire 51 per cent shares in foreign oil operations and on Thursday Nicolas Maduro, the country's foreign minister, said the government was also considering nationalising the mining industry.
Left-wing politician Juan Montenegro Nunez told the National Assembly: "This process is unstoppable. This process is an historic necessity."
The latest measure comes after Chavez called for a constitutional amendment to remove any limit on presidential terms.
Gerardo Blyde, an opposition politician criticised the proposed law, saying: "What is becoming evident is that all the powers are one single power in Venezuela - Hugo Chavez."
Teodoro Petkoff, the campaign manager for Chavez' defeated presidential opponent Manuel Rosales, said: "In an environment of obsequiousness and servility, 'I, the Supreme [Chavez] am ready to legislate, backed by this far-reaching, enabling law."
The law, Petkoff said in a column published in the daily Tal Cual, allows Chavez to legislate "without any debate in the country."