It is the first time the women's and men's T20 World Cups will be held as standalone events in the same year and in the same country.
Pakistan, South Africa and a qualifier complete England's women's group.
The competition begins on 21 February, with the final at the MCG on 8 March.
With the final on International Women's Day, organisers are hoping to attract a world record attendance for a women's sporting fixture.
Hosts Australia make up the other group with New Zealand, India, Sri Lanka and another qualifier.
England women's group fixtures: v South Africa (Perth, 23 Feb); qualifier (Canberra, 26 Feb); Pakistan (Canberra, 28 Feb); West Indies (Sydney, 1 Mar)
Full women's tournament fixtures and venues
Afghanistan's Rashid Khan, Australia's Alex Carey and England's Tom Curran with the Men's T20 World Cup
England seamer Tom Curran (right), who is playing in Australia's Big Bash League, was among the players at the announcement
Later in the year, the England men's side will also face Afghanistan and two qualifiers in the Super 12 stage.
Hosts Australia face Pakistan, the world's top-ranked team, in the opening match of the other Super 12 group, which also includes West Indies, New Zealand and two more qualifiers.
Afghanistan had clinched the last of the automatic Super 12 places, which were based on the International Cricket Council's (ICC) rankings on 31 December 2018.
Sri Lanka and Bangladesh, who just missed out, must compete in the first round alongside six teams who make it through the ICC Global Qualifier - which could include Ireland and Scotland.
The tournament - formerly known as the World Twenty20 - begins on 18 October 2020, culminating with the final at the MCG on 15 November.
England men's Super 12 fixtures: v qualifier (Perth, 26 Oct); South Africa (Sydney, 30 Oct); India (Melbourne, 1 Nov); Afghanistan (Brisbane, 4 Nov); qualifier (Adelaide, 7 Nov)
