His mother was Margaret Matilda, daughter of James Talbot, while Lawrence Dundas, 1st Marquess of Zetland, was his elder brother.
When his elder brother succeeded in the earldom of Zetland in 1873, Dundas was granted the rank of a younger son of an earl, and thus styled the Honourable John Dundas.
Dundas was returned to Parliament for Richmond, Yorkshire, in 1873 (succeeding his elder brother), a seat he held until 1885.
Alice Louisa, daughter of Charles Wood, 1st Viscount Halifax, in 1870.
His wife survived him by over 40 years and died in June 1934.