Peterson was born on August 15, 1925, in Montreal, Quebec, Canada, to immigrants from the West Indies (Saint Kitts and Nevis and the British Virgin Islands): his mother, Kathleen, was a domestic worker; his father, Daniel, worked as a porter for Canadian Pacific Railway and was an amateur musician who taught himself to play the organ, trumpet and piano. Peterson grew up in the neighbourhood of Little Burgundy in Montreal. It was in this predominantly black neighbourhood that he encountered the jazz culture. At the age of five, Peterson began honing his skills on trumpet and piano, but a bout of tuberculosis when he was seven years old prevented him from playing the trumpet again, so he directed all his attention to the piano. His father was one of his first music teachers, and his sister Daisy taught him classical piano. Peterson was persistent at practicing scales and classical études.
As a child, Peterson studied with Hungarian-born pianist Paul de Marky, a student of István Thomán, who was himself a pupil of Franz Liszt, so his early training was predominantly based on classical piano. However, Peterson was captivated by traditional jazz and boogie-woogie and learned several ragtime pieces. He was called "the Brown Bomber of the Boogie-Woogie".
At the age of nine, Peterson played piano with a degree of control that impressed professional musicians. For many years his piano studies included four to six hours of daily practice. Only in his later years did he decrease his practice to one or two hours daily. In 1940, at fourteen years of age, he won the national music competition organized by the Canadian Broadcasting Corporation. After that victory, he dropped out of the High School of Montreal, where he played in a band with Maynard Ferguson. Peterson became a professional pianist, starring in a weekly radio show and playing at hotels and music halls. In his teens, he was a member of the Johnny Holmes Orchestra. From 1945 to 1949, he worked in a trio and recorded for Victor Records. He gravitated toward boogie-woogie and swing with a particular fondness for Nat King Cole and Teddy Wilson. By the time Peterson was in his 20s, he had developed a reputation as a technically brilliant and melodically inventive pianist.