Mr. Curran had been weakened by lung and kidney problems and underwent dialysis three days a week the last few years but rarely missed a day at school, let alone a game or practice.
He broke his kneecap last month when he slipped on ice while on his way to church. The mishap did not prevent him from attending church that day.
"He had the respect of so many young players, and the older players would come back to see him," Archbishop Molloy president Richard Karsten said.
Those former players included some of New York City's biggest names in high school basketball - 1972 Olympian Kevin Joyce; Brian Winters; Kenny Smith; Kenny Anderson; and Russ Smith, who was playing for Louisville on Thursday night in the Big East quarterfinals at Madison Square Garden.
Anderson, who went on to play at Georgia Tech and in the NBA, tweeted: "I lost my favorite coach, mentor and just a great soul Jack Curran you will be missed."
New York Mets outfielder Mike Baxter played for Mr. Curran from 2000 to 2002. He remembered the coach not only as an "incredible storyteller" but someone who always had his players' interests at heart.
Mr. Curran, who lived in Rye, N.Y., played minor-league baseball for the Dodgers and Phillies.
"I'm not sure in my life there is anybody who has more of an impact on my life than Mr. Curran," said Whitey Rigsby, a member of Molloy's city championship basketball teams in 1973 and 1974 and who went on to play at Villanova and still works in athletic development at the school.
Mr. Curran's teams won five city championships in basketball and 17 in baseball. No other New York City coach has ever won a title in both sports in the same year. Mr. Curran did it four times - 1969, 1973, 1974, and 1987. His record was 972-437 in basketball and 1,708-523 in baseball.
"Those marks will never be broken," Karsten said.
Mr. Curran is the only high school coach in the New York state Hall of Fame in both basketball and baseball, Karsten said. He is the only coach to be selected national coach of the year in two sports.
Funeral arrangements were not announced.