He will be honoured for his "compassionate service, courageous witness and inspiring leadership in relation to LGBTQ+ Catholics", the alliance said in a statement on Tuesday.
The award is to be presented to him on 15 November.
Stowe has headed the Lexington diocese since 2015. Since then, he has been a "consistent and strong supporter" of LGBTQ+ people in the church, the press release continued.
In addition to his participation in relevant events, he supports help for vulnerable young people, even if this means going against the vote of the US bishops' conference. He has also distinguished himself by accepting a trans man as a diocesan hermit.
This makes him the first openly transgender hermit in the world to live in his diocese.
Prize for understanding
The Alliance awards the prize to people whose work promotes dialogue, understanding and reconciliation between sexual minorities and the Church. It has been awarded since 1992.
"New Ways Ministry" is an advocacy organisation for lesbian, gay, bisexual and transgender Catholics in the USA.
The organisation was founded in 1977 by the nun Jeannine Gramick and Father Robert Nugent.
The aim of the group is to create acceptance for queer Catholics within the church.