McMaster was also a Stenhousemuir director and stepped down as Scottish Football League president through ill health in 2009.
A Thistle statement read: “Over an almost 20-year period, Brown not only served as a director and vice-chairman, but was also chairman on two separate occasions.
“In his first spell at the helm of the club, Brown led Thistle through one of the most difficult times in its history during the Save the Jags campaign.
“Brown was a passionate football man and, in addition to his time at Thistle, spent two and a half years as president of the Scottish Football League.
“The thoughts of everyone at Partick Thistle Football Club are with Brown’s family and friends, especially his wife, Jean, and his children, Scott, Craig, Jill and John.”