Only about 25% of registered voters cast a ballot.
A two-thirds majority in parliament will allow Mr Chavez to remove the current constitutional limit of two presidential terms in office.
But the opposition says the low turnout deprives the election of legitimacy.
"Venezuela is speaking with its silence," said Julio Borges, a prominent opposition member. ...............***
Several of Venezuela's major opposition parties boycotted the vote on Sunday, which had an estimated turnout of 25 percent and is likely to further polarize Venezuelan society. The country has been deeply divided by the leftist leader's rhetoric, his alliance with the Cuban leader Fidel Castro and his efforts to seize unproductive farms for poor farmers, start state-funded cooperatives and expand social programs for the poor.
"Silence united Venezuelans," said Gerardo Blyde of Justice First, one of several leading opposition parties that pulled out days before the vote, complaining the voting system could not be trusted. ............***