Stoker was born on 8 November 1847 at 15 Marino Crescent, Clontarf, on the northside of Dublin, Ireland. His parents were Abraham Stoker (1799–1876), from Dublin, and Charlotte Mathilda Blake Thornley (1818–1901), who was raised in County Sligo. Stoker was the third of seven children, the eldest of whom was Sir Thornley Stoker, 1st Bt. Abraham and Charlotte were members of the Church of Ireland Parish of Clontarf and attended the parish church with their children, who were baptised there.
Stoker was bedridden with an unknown illness until he started school at the age of seven, when he made a complete recovery. Of this time, Stoker wrote, "I was naturally thoughtful, and the leisure of long illness gave opportunity for many thoughts which were fruitful according to their kind in later years." He was educated in a private school run by the Rev. William Woods.