The club legend died from injuries that he sustained in a fall, with Villa announcing the news through a statement.
Shaw was part of a legendary team at the club, helping Villa win the 1981 league title and the European Cup in 1982.
"Aston Villa Football Club is deeply shocked and profoundly saddened to learn that Gary Shaw, one of our European Cup-winning heroes, has passed away," the club said on Monday.
"Gary was one of our own, a talented striker who delighted supporters with his goalscoring exploits which helped fire Villa to success in the 1980s. Individual accolades would also follow for a player who was idolized by many on the terraces.
"He passed away peacefully earlier today surrounded by his family, who asked Aston Villa to release a statement on their behalf.
"The thoughts of everyone at the club are with Gary's family and loved ones at this extremely difficult time."