Schultz, who battled illness in recent months, is an Australian Football Hall of Fame member.
The former champion ruckman, known as Gentleman John, was one of the Bulldogs' greatest players and was renowned for his integrity and fairness.
He played 188 VFL games for the club - then known as Footscray - and won the 1960 Brownlow Medal.
He also represented Victoria 24 times, won All-Australian honours in 1961 and claimed five club best-and-fairest awards.
Schultz was the Bulldogs' best player in their losing 1961 grand final and was named in the club's Team of the Century.
He later mentored the Bulldogs' playing and coaching groups and was a club ambassador.
Schultz memorably presented the AFL premiership cup to Bulldogs coach Luke Beveridge and players Bob Murphy and Easton Wood after the club's drought-breaking grand final win in 2016.
AFL chief executive Andrew Dillon said the league was "deeply saddened" by Schultz's passing and sent his condolences to his family.
"John was a great, great player ... but he was someone too always with a smile and a good word for every occasion," Dillon said in a statement.
"He was a regular fixture at the Brownlow Medal, as one of our older greats, and took great pleasure each year at the Hall of Fame to welcome new inductees, and congratulate them on their careers and achievements, while always modestly turning the conversation away from his own great career.
"John was one of the few great links that our game still had to the 1950s and 1960s and he retained incredible enthusiasm for football, the players, the fans and the excitement of a match day.
"His smile on grand final day in 2016, when he handed over the cup, lit up the entire ground and we send our best wishes to his family, his many, many friends and all at the Western Bulldogs."
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