Haefner, who made his fortune selling cars and treasured his privacy, was for decades a key figure for the Islandia-based software maker.
Aside from being the largest shareholder, Haefner was a longtime adviser to the company's founder, Charles Wang. And he was a crucial player 11 years ago in helping CA fight off a takeover attempt by Texas billionaire Sam Wyly.
"We valued his insight and knowledge of our business and he will be missed," CA said Wednesday in a statement.
It remains unclear what, if any, impact Haefner's death will have on CA. He owned 26.6 percent of the company, which is the world's second-largest maker of mainframe computer software, and has the largest stock-market value of any company on Long Island.
Haefner's $3.1 billion in shares are held in an investment vehicle, Careal Holding, where his son Martin continues to play a central role. In a statement forwarded by CA, the vehicle indicated it had no immediate plans to sell the stock, saying it "expects no change in the relationship between CA Technologies and Careal Holding."
News of Haefner's death came as CA grapples with fallout from computer problems following a software upgrade for a major customer, Royal Bank of Scotland.
RBS has said it is still seeking to determine what caused the weeklong glitch, which delayed posting credits and debits for millions of customers, and which could cost the bank $156 million in staff overtime and compensation claims.
Both CA and RBS said they were working to resolve the issue. "We have been clear we will fully investigate the causes of this incident," RBS spokesman Ed Canaday said.
The software troubles at RBS do not appear to be rattling CA investors, however. The company's stock price is virtually unchanged from one week ago and climbed 0.96 percent Wednesday, to $26.38 a share.
The son of a missionary, Haefner was born in Zurich. He founded a car dealership in 1945 and built it into one of Switzerland's main importers. Haefner also bred racehorses, including Go And Go, winner of the 1990 Belmont Stakes.
Haefner first invested in computers in 1976, buying a stake in a Dallas company. It was acquired in 1987 by CA, then known as Computer Associates. Haefner guarded his shares closely over the next few decades. And every few months, he hosted Wang in Zurich to talk strategy.
That relationship became key in 2001 when investor Sam Wyly tried to force Wang from the helm. But the Texan couldn't best Haefner and his big holdings in the company.
Yet for all his influence, Haefner shunned the spotlight and rarely granted interviews.
"Mr. Haefner isn't into people with cameras," J. Stan Cosgrove, who ran Haefner's horse farm in Ireland, told Newsday in 2001. "He's a private man, a humble man."