Citing his wife, Evelyn, a statement on the team's Web site said Antwine died in Memphis early in the day.
"This is a really sad day," Patriots Chairman and Chief Executive Officer Robert Kraft said in a written statement. "In the 1960s, the defensive tackle tandem of 'Twine' and Jim Lee Hunt were as good as any in the league and helped propel the Patriots to the franchise's first division championship in 1963."
Antwine was a six-time All-Star in the old American Football League and was named to the Patriots' All-Decade Team for the 1960s.
Antwine broke in with the Houston Oilers in 1961 and was then traded to the Patriots, for whom he played 11 of his 12 seasons as a pro. He played in 142 regular-season games as a pro before retiring with the Philadelphia Eagles in 1972.
There was no announcement regarding funeral plans.