The 1982 European Cup winner had been hospitalised due to a head injury from a fall.
Shaw made 213 appearances for his boyhood club and scored 79 goals.
He is regarded as one of Villa's best forwards in the club's 150-year history.
Villa announced the tragic news in a club statement and paid tribute to one of the heroes of their 1982 triumph.
Shaw (left) began his career with Aston Villa and went on to win three trophies with the club
'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,' the statement read.
'Individual accolades would also follow for a player who was idolised 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.'