Minchin was educated at Christ Church Grammar School, an independent school in Perth. He graduated from the University of Western Australia (UWA) in 1996 with a Bachelor of Arts degree in English and theatre, and from the Western Australian Academy of Performing Arts in 1998 with an Advanced Diploma in Music (Contemporary Music). In 2013, he was awarded an honorary degree of Doctor of Letters from UWA. In 2015, he was awarded a second Honorary Doctor of Letters, along with Dennis Kelly, from Mountview Academy of Theatre Arts.