"On an almost daily basis, we are being described the worst threat - be it to Nato as a whole, or to Europe, America or other countries," Mr Medvedev said.
He cited Nato chief Jens Stoltenberg's speeches and films depicting Russia starting a nuclear war.
"Sometimes I wonder if this is 2016 or 1962," Mr Medvedev said.
The Cold War was a period of ideological confrontation between the former Soviet Union and Western countries. It began after World War Two and ended with the collapse of the Soviet-led communist camp in the 1989.
The 45 years of tension were marked by espionage and proxy wars involving client states - all undertaken with the knowledge or fear of the nuclear catastrophe that actual war would bring.
The Nato alliance was established in 1949 to protect Western countries.
The six key moments of the Cold War relived
How the Cold War ended, in 1989
BBC News - Could you stop World War Three-
Russia has recently come under strong criticism over its air strikes in support of Syrian President Bashar al-Assad and over its role in neighbouring Ukraine, which culminated with the annexation of the Crimean Peninsula in 2014.
In an interview with the BBC at the same Munich conference, Mr Stoltenberg said Russia had changed borders by force and had become more assertive - and that Nato had to be able to respond to threats.
"We are not in a cold-war situation, but also not in the partnership that we established at the end of the Cold War," Mr Stoltenberg said.
Nato, he said, did not want an escalation, but enhanced political dialogue with Russia.
Early this month, the BBC broadcast a programme entitled World War Three: Inside the War Room, which imagines a hypothetical Russian attack on its Baltic neighbours - Nato members - and nuclear confrontation.

The south will have three teams, with one based at The Oval with Surrey, who pipped a joint bid by Middlesex and the MCC for the one London spot.
There will also be a team based in the south west and another in Hampshire.
The north will have two sides, in Lancashire and Yorkshire, while the Midlands team for the Twenty20 league will be at Loughborough University.
Loughborough is also the long-term base of the England women's team.
All six hosts have been awarded hosting rights for a four-year period from 2016-2019.
The tournament will be played in a Twenty20 format this season, before adding a 50-over competition in the future.
The group stage of the 2016 competition will run from 30 July to 14 August, with the top four teams qualifying for a finals day.
Further details, including team names, will be revealed at a later date.
"This is a key day in the creation of the Women's Cricket Super League," said England & Wales Cricket Board chief executive Tom Harrison.
"The bidding process for obtaining the hosts was competitive from the outset."
There were 28 initial expressions of interest for the WCSL.
Hampshire Cricket with partners: Berkshire Cricket Ltd, Dorset Cricket Board, Isle of Wight Cricket Board, Oxfordshire Cricket, Southampton Solent University, Sussex Cricket Ltd, Wiltshire Cricket Ltd
Lancashire County Cricket Board with partners: Lancashire County Cricket Club, Lancashire County Cricket Club Foundation
Loughborough University
South West: Somerset County Cricket Club, Gloucestershire County Cricket Club, University of Exeter
Surrey County Cricket Club
Yorkshire County Cricket Club
Russian Prime Minister Dmitry Medvedev has said strains between Russia and the West have pushed the world "into a new cold war".
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The six team hosts for this summer's inaugural Women's Cricket Super League have been announced.