Lights first went off as Ramon Lobo, a pro-government lawmaker, defended the energy policies of President Nicolas Maduro, reports said.
Opposition MP Luis Florido quipped on Twitter: "The country's reality has hit them in the face."
The session was later suspended. Venezuela faces a severe electricity crisis and shortages are frequent.
Reports said other buildings in the same area of the capital, Caracas, were also hit by power cuts, on Wednesday afternoon.
Venezuela's National Assembly is controlled by the opposition.
Delsa Solorzano, an opposition MP, tweeted a video of the chamber in the dark.
MP Freddy Guevara, also from the opposition, said: "What a shame: the parliament session was interrupted because the energy went off. Right on the day we're discussing the energy sector law."
Oil-rich Venezuela is in the middle of a deep economic crisis caused by a drop in global oil prices. The country is suffering from a shortage of basic goods, food and electricity.
Earlier this year, the government introduced power rationing and a two-day working week for public sector workers as ways to tackle the crisis.
It said a major drought, which dramatically reduced water levels at its main hydroelectric dam, was to blame. But the opposition accused authorities of mismanagement.
Some of the measures have already been lifted.
A power cut left Venezuela's parliament in the dark as it discussed a law dedicated to the energy sector.