"More than 85% of Venezuelans did not obey this regime and said 'no'," Machado said about those who abstained.
Independent journalists who visited polling stations throughout the day said that they saw no queues and fewer people turning out than for the presidential election last July.
The CNE meanwhile put the turn-out at 42.6%.
The opposition has long questioned the independence of the CNE, which is led by Elvis Amoroso, a former legal counsel to President Maduro.
The CNE came in for widespread international criticism in last year when it declared Mr Maduro the winner of the presidential election without ever providing the detailed voting tallies to back up their claim.
Venezuela's opposition, meanwhile, published voting tallies it had gathered with the help of official election observers which showed that its candidate, Edmundo González, was the overwhelming winner.
Amid the wave of repression and arrests which followed the presidential election, González went into exile to Spain.
Machado, who threw her weight behind presidential hopeful Edmundo González after she was barred from running for public office, remained in Venezuela.
She was the main advocate for boycotting this Sunday's legislative and gubernatorial elections, saying that the result of July's presidential election should be respected before any new elections are held.
"We voted on 28 July. On 25 May, we won't vote," she said in a video message shared earlier this month.
However, a handful of opposition politicians did run for office, arguing that leaving the field open to government candidates was a mistake.
Among them were former presidential candidate Henrique Capriles, Zulia state governor Manuel Rosales and Juan Requesens, who was jailed by the Maduro government for allegedly taking part in a 2018 drone attack on the president.
Capriles told Spanish daily El País that for him "voting in Venezuela is an expression of resistance, of resilience, of not giving up".
Their decision to stand in the elections was criticised by those calling for a boycott, with Machado saying they had "betrayed the cause".
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