Born in Pittsburgh, Pennsylvania, Heinz was the son of Henry J. Heinz II, heir to the H. J. Heinz Company. After graduating from Phillips Exeter Academy in 1956 and Yale University in 1960, he earned an MBA from Harvard Business School in 1963. In 1963, Heinz enlisted in the United States Air Force and served on active duty from June to December of that year at Lackland Air Force Base. He then served with the 911th Troop Carrier Group, based at the Greater Pittsburgh Airport, as a member of the United States Air Force Reserve; he was honorably discharged in 1969 with the rank of staff sergeant.

From 1970 to 1971, Heinz was a member of the faculty at the Graduate School of Industrial Administration at Carnegie Mellon University. His career as a businessman included positions as an analyst in the controller's division, and numerous positions in the marketing division of the H. J. Heinz Company.

In 1971, he was elected by special election to fill the vacancy caused by the death of Robert J. Corbett during the Ninety-second Congress. He was reelected to the Ninety-third and Ninety-fourth Congresses. Heinz was elected to the Senate in 1976 and reelected in 1982 and 1988.

Heinz's initial election to the Senate was aided by the U.S. Supreme Court's decision, Buckley v. Valeo, issued mid-campaign, which invalidated the Congressionally-placed restrictions on the spending of one's own personal funds in a political campaign. (See campaign finance.) Heinz spent millions of dollars attacking Democratic nominee William J. Green, a young seven term congressman from Philadelphia and future mayor of that city, as being "soft" on military issues because he had voted against various Defense appropriation bills in the Vietnam War era.

Heinz's Senate work was focused on retirement and the elderly, health care, international trade, finance and banking, environmental issues, human development and education. He was chairman of the National Republican Senatorial Committee (Ninety-sixth and Ninety-ninth Congresses) and a member of the Senate Special Committee on Aging (Ninety-seventh through Ninety-ninth Congresses).

Heinz and six other people were killed on April 4, 1991, when a Bell 412 SP helicopter collided with the Senator's Piper Aerostar plane over Merion Elementary School in Lower Merion Township, Pennsylvania. All aboard the two aircraft and two children playing outside the school were killed. The helicopter had been dispatched to check out a problem Heinz's plane was having with its landing gear. While moving in for a closer look, the helicopter's rotor blades struck the bottom of the plane, causing both aircraft to lose control and crash. (Interestingly, former U.S. Sen John Tower was killed in a plane crash in Brunswick, Georgia, the very next day.)

He was interred in the Heinz family mausoleum in Homewood Cemetery, Pittsburgh.

The John Heinz National Wildlife Refuge at Tinicum was renamed following his death. The 1,200 acre (4.9 km²) refuge includes the largest remaining freshwater tidal marsh in Pennsylvania as well as other habitats that are home to a variety of plants and animals native to Southeastern Pennsylvania.

His widow, Teresa, is now married to Senator John Kerry. She was introduced to Kerry by Heinz at an Earth Day rally in 1990. The principal beneficiary of Heinz's estate, she has been extremely active in expanding his legacy through philanthropy.

Several institutions bear his name, including: