The 18-year-old batter, who was awarded her first professional contract with Hampshire last month, will lead the team at the tournament which begins on 18 January.
Sixteen teams from around the world will take part in the 41-match event across 15 days of competition until 2 February 2025.
Drawn in Group B, England take on Ireland (Saturday 18 January), Pakistan (Monday 20 January) and USA (Wednesday 22 January) with all group B matches in Johor.
Norgrove said: “I am absolutely thrilled to be given the opportunity to lead the squad in the World Cup and honoured to represent my country in such an amazing competition. We can’t wait to get going as a team.”
Head coach Chris Guest added: “We are delighted to have Abi leading the side into the World Cup. She has shown great leadership qualities in both the Sri Lanka tour and preparation phase for the World Cup. Abi has gained significant experience of senior domestic cricket this season which I’m sure she will draw upon in Malaysia.”
England Women U19 squad for ICC U19 Women's T20 World Cup
Abi Norgrove (captain; Hampshire)
Phoebe Brett (Warwickshire Academy)
Olivia Brinsden (Lancashire Thunder Academy)
Tilly Corteen-Coleman (Surrey)
Trudy Johnson (Durham)
Katie Jones (Somerset)
Charlotte Lambert (Surrey)
Eve O’Neill (Vipers Academy)
Davina Perrin (Warwickshire)
Jemima Spence (Surrey)
Charlotte Stubbs (Surrey Academy)
Amuruthaa Surenkumar (Warwickshire)
Prisha Thanawala (The Blaze)
Erin Thomas (Yorkshire)
Grace Thompson (Durham Academy)