Six people were also injured in the escalating violence, the public ministry said in a statement on Friday. The latest figures raised the total number of deaths during growing protests to 20 over the past three weeks.
Venezuelan Vice President Tareck El Aissami said on Friday the country is facing what he calls an "unconventional war" led by opposition groups working in concert with criminal gangs.
Riot police firing tear gas fought running street battles in the east, west, and south of Caracas with demonstrators demanding the removal of Maduro, witnesses quoted by AFP news agency said.
The public ministry said 11 people died in El Valle - a working class neighbourhood near Caracas' biggest military base - all men between the ages of 17 and 45. Another death was reported east of Caracas in El Sucre.
A probe was ordered "to investigate the deaths of 11 people and the injuries caused to six others", the ministry said.
Opposition leaders said some people were hit with an electrical current in El Valle while trying to loot a bakery protected by an electric fence.
Resident Carlos Yanez said the scene was "like a war".
"The police were firing tear gas, armed civilians were shooting guns at buildings. My family and I threw ourselves to the floor. It was horrible," said the 33-year-old construction worker.
The opposition accuses the left-wing government of sending gangs of armed thugs to attack them, and says security forces have been repressing protesters.
Video taken by locals showed residents throwing bottles and other objects out their windows at the gunmen in the streets below, shouting "murderers".
At one point, demonstrators throwing Molotov cocktails managed to set fire to one of the armoured police trucks firing tear gas at them, lighting up the night sky.
There was a heavy security presence Friday on the streets of Caracas, as residents and workers cleaned up the destruction left by the clashes and bouts of looting.
The two sides looked set to spend the day regrouping after massive protests Wednesday and Thursday erupted into unrest in the flashpoint western city of San Cristobal and several other cities.
Call for more protests
Opposition leaders have called new protests for Saturday and Monday.
On Saturday, they plan to march in silence to the Catholic Church's episcopal seats nationwide. They also intend to erect roadblocks on Monday to grind the country's traffic to a halt.
Protesters blame Maduro - heir of the leftist Bolivarian Revolution launched by the late Hugo Chavez in 1999 - for an economic crisis marked by severe shortages of food, medicine, and basic goods.
Maduro says the protests seeking to remove him are part of a United States-backed coup plot.
On Thursday, the president said the opposition had agreed to new talks, but his opponents denied the claim, saying the only way forward was new elections.
Senior opposition leader Henrique Capriles slammed Maduro as a "dictator" and "mythomaniac".