Victims are arrested and shot, with crime scenes manipulated to suggest they resisted police, a report says.
The UN urges Venezuela to end the "grave violations of economic, social, civil, political and cultural rights".
Venezuela's government has called the report distorted and biased.
Mr Maduro is locked in a political battle with opposition leader Juan Guaidó.
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Mr Guaidó, head of the country's National Assembly, declared himself interim president in January and has the backing of more than 50 countries, including the US and most of Latin America. Mr Maduro retains the loyalty of most of the military and important allies such as China and Russia.
Some four million people have fled Venezuela since 2015, according to the UN, amid a severe economic crisis that has resulted in high unemployment and chronic shortages of food and medicine.
What is the UN report and what does it allege?
The report is scheduled to be presented to the UN Human Rights Council on Friday.
It is based on "558 interviews with victims and witnesses of human rights violations and the deteriorating economic situation" from January 2018 to May 2019.
Its most damning findings relate to the number of deaths the Venezuelan government has ascribed to resisting arrest.
That figure for last year was 5,287, with another 1,569 up to 19 May this year.
Referring to these figures as "unusually" and "shockingly" high, the report says: "Information analysed by Office of the United Nations High Commissioner for Human Rights suggests many of these killings may constitute extrajudicial executions."
The UN says witnesses reported how the Special Action Forces (FAES) "manipulated the crime scene and evidence. They would plant arms and drugs and fire their weapons against the walls or in the air to suggest a confrontation and to show the victim had 'resisted authority'".
It adds that the UN "is concerned the authorities may be using FAES and other security forces as an instrument to instil fear in the population and to maintain social control".
The BBC's Imogen Foulkes in Geneva says the report paints a dark picture of Venezuela, in which unmarked black vans arrive in poor neighbourhoods, masked officers get out, round up young men and shoot them.
How has Venezuela responded?
Venezuela's government received an advance copy of the report and issued an 11-page response on Thursday, detailing various points it considered as errors.
It said the UN was wrong to say the state was not investigating alleged human rights violations, adding that several suspects had been imprisoned.
It also complained that the majority of the report's interviews were conducted with Venezuelans in exile, and disputed the use of the phrase "humanitarian crisis", insisting it was an economic crisis, which has been provoked by US, EU and Canadian sanctions.
What are the other allegations?
The lengthy UN report also covers areas such as economic and social rights, and social programmes and policies.
Problems of access to justice - which the report says the government has asked for help with - are also tackled.
A separate section covers the rights of indigenous people, and migrants and refugees.
The UN concludes it believes "there are reasonable grounds to believe that grave violations of economic and social rights, including the rights to food and health, have been committed in Venezuela".
On accusations of torture it says detainees have been subjected to "one or more forms of torture or cruel, inhuman or degrading treatment or punishment, including electric shocks, suffocation with plastic bags, water boarding, beatings, sexual violence, water and food deprivation, stress positions and exposure to extreme temperatures".
Wasn't there a recent high-profile case?
Yes. A navy captain arrested over an alleged plot to assassinate President Maduro died in custody with his lawyer alleging it was as a result of torture.
The death sparked outrage, coming just days after the visit to Venezuela by UN human rights chief, Michelle Bachelet.
Local media say the official autopsy reported that the body of Rafael Acosta, 49, had showed signs of having been subjected to extreme force, had been starved of oxygen and had suffered severe beatings and electrocution.
Two men, Lt Ascanio Tarascio and Sgt Estiben Zarate have been charged with murder.
What's the current political situation?
President Maduro has intensified a crackdown on the opposition since a failed military uprising against him in April led by Mr Guaidó.
Since the failed rebellion, described by Mr Maduro as part of a US-orchestrated coup, many opposition MPs have lost their parliamentary immunity and some have been arrested.
While Mr Guaidó's parliamentary immunity has been lifted, he has so far not been jailed, even though he recently said he did not rule out the use of military force to oust Mr Maduro from power.