The Bears confirmed Suhey died on Sunday morning. No other details were provided.
Suhey played for Chicago for 10 seasons after he was selected by the Bears in the second round of the 1980 draft. He helped clear the way for Payton to become the NFL's career leading rusher, a record Payton held until Emmitt Smith surpassed his total on Oct. 27, 2002.
Suhey and Payton were close friends. Payton served as the godfather for Suhey's youngest son, Scott.
"After we lost my dad in 1999, Matt became the biggest father figure I had," Walter's son, Jarrett, posted on social media on Monday. "When everything felt uncertain, he was there. My dad left him in charge and Matt never let that responsibility sit lightly. He protected our family. He looked after us. He made sure we were okay, year after year, without ever making it about himself.
"That is who he was."
Though often more comfortable out of the spotlight, Suhey was known for being articulate and supportive of teammates. He frequently spoke on behalf of others, including Payton, and more recently appeared at Hall of Fame induction events honoring former Bears offensive lineman Jimbo Covert.
Fred Mitchell, a former Chicago Tribune sportswriter who covered the Bears during that era, said Suhey's legacy extended beyond his accomplishments on the field.
"His legacy will include, obviously, the fact that he was best friends with Walter Payton and that he was, sort of an understated personality on a Super Bowl Bears team that was full of great vicarious, personalities from Jim McMahon, Steve McMichael, and, on and on," Mitchell said.
Suhey was Chicago's second-leading rusher when the Bears went 15-1 during the 1985 regular season, finishing with 471 yards on the ground. Payton rushed for 1,551 yards and nine touchdowns that year.
The 1985 Bears shut out the New York Giants and Los Angeles Rams in the playoffs before routing New England 46-10 in the Super Bowl. Suhey scored the first TD against the Patriots on an 11-yard run in the first quarter. He finished with 52 yards on 11 carries, and he also had a 24-yard reception.
The durable Suhey played in 148 regular-season games during his 10 years with the Bears, starting 100. He had 828 carries for 2,946 yards and 20 touchdowns. He also had 260 receptions for 2,113 yards and five TDs.
No cause of death has been released, and those who knew him said they were unaware of any recent illnesses.
ABC7 contributed to this report.