June Wright was born June Healy, daughter of Dora and Gerald Healy, in the Melbourne suburb of Malvern. Some newspaper articles suggest her grandfather, John Healy, was a Melbourne writer, who also wrote as 'An Onlooker'. Both her grandfather and father appear to have been successful cricketers (to the Sheffield Shield level), but this has not yet been confirmed.
Wright was educated at Brigidine Convent (later named Kildara) and Vaucluse College, both in Melbourne, Loreto (Maryyatville, Adelaide) and Mandeville Hall (Toorak, Melbourne).
As a young woman, she worked in the Melbourne Central Telephone Exchange, the setting for her first novel (Murder in the Telephone Exchange). Following her marriage to Stewart Wright, and the birth of her first son, Patrick, she began writing. She published a further five novels but largely relinquished her literary career in the mid-1960s after a breakdown in her husband's health.
Wright returned to writing in the early 1990s. A three-volume autobiography (The Collected Works of June Wright : Non-Fiction) was privately published.