Heinz was one of eight children born to John Henry and Anna Schmidt Heinz. Both parents had emigrated from Germany and settled in the Birmingham section of Pittsburgh, Pennsylvania—today known as the South Side.

When Henry was five the family moved several miles up the Allegheny River to the little town of Sharpsburg. There, at age six, young Henry (Called Harry by his family) started helping his mother tend a small backyard garden behind the family home. At age eight Henry was canvassing the neighborhood with a basket under each arm selling vegetables from the family garden door to door.

By age nine he was growing, grinding, bottling and selling his own brand of horseradish sauce. At ten he was given a ¾ acre (3,000 m²) garden of his own and had graduated to a wheelbarrow to deliver his vegetables. At twelve he was working 3½ acres (14,000 m²) of garden using a horse and cart for his three-times-a-week deliveries to grocery stores in Pittsburgh. At seventeen he was grossing $2,400 a year—a handsome sum for the times.

Heinz attended a business college and after graduating started employment with his father's brick-manufacturing business, eventually becoming a partner in the firm. All the while he continued growing and selling fresh produce.

In 1869, Heinz founded Heinz Noble & Company with a friend, L. C. Noble, and began marketing horseradish. The company went bankrupt in 1875, but the following year Heinz founded another company, F & J Heinz, with his brother and a cousin. One of this company's first products was tomato ketchup.

The company continued to grow, and in 1888 Heinz bought out his other two partners and reorganized the company as the H J Heinz Company, the name it carries to the present day. Its famous slogan, "57 varieties," was introduced by Heinz in 1896. Inspired by an advertisement he saw while riding an elevated train in New York City (a shoe store boasting of "21 styles"), Heinz picked the number more or less at random because he liked the sound of it, selecting 7 specifically because, as he put it, of the "psychological influence of that figure and of its alluring significance to people of all ages." (The company marketed far more than 57 varieties of product even at that point.)

H J Heinz was incorporated in 1905, and Heinz served as its first president, remaining in the position for the rest of his life. Under his tutelage, the company was noted for fair treatment of workers and for pioneering safe and sanitary food preparation. Heinz led a successful lobbying effort in favor of the Pure Food and Drug Act in 1906. He also was very involved working in his church's Sunday school and in various philanthropic endeavors, notably the Sarah Heinz settlement house in Pittsburgh, which he founded in 1894 and named after his wife.

At the time of his death in Pittsburgh at the age of 74, the company had over twenty food processing plants, and also included seed farms and container factories. Heinz was the great-grandfather of Pennsylvania Senator John Heinz.