Druitt was born in Wimborne Minster, Dorset, England. He was the second son and third child of prominent local surgeon William Druitt, and his wife Ann ("née" Harvey). William Druitt was a justice of the peace, a governor of the local grammar school, and a regular worshipper at the local Anglican church, the Minster. Six weeks after his birth, Montague Druitt was christened at the Minster by his maternal great-uncle, Reverend William Mayo. The Druitts lived at Westfield House, which was the largest house in the town, and set in its own grounds with stables and servants' cottages. Druitt had six brothers and sisters, including an elder brother William who entered the law, and a younger brother Edward who joined the Royal Engineers.