President Nicolas Maduro promptly rejected the demand, the latest offensive in the battle to replace the government over a crisis that has families queuing up for food rations.
"We are facing the worst food emergency in Venezuela's history," said Ismael Garcia, the lawmaker leading the motion to sack minister Rodolfo Marco Torres.
The speaker of the opposition-controlled National Assembly, Henry Ramos Allup, said the government must remove Torres from his post after two-thirds of the lawmakers present approved a no-confidence motion against him.
He even threatened to cut the power to the legislature, as part of widespread blackouts he has imposed to save power.
More From This Section
His opponents meanwhile said they had gathered more than five times the 200,000 signatures needed to begin organizing a referendum to remove Maduro.
Senior opposition leader Henrique Capriles said more than a million people had signed a petition calling for a recall referendum.
The signatures will be handed over to the National Electoral Board (CNE) early next week for verification.
The political tension, shortages and now enforced electricity blackouts that started this week have raised fears of unrest in the South American oil state.
Looting and clashes were reported in towns including the country's second-biggest city Maracaibo after daily power cut-offs were formally launched on Monday.