Villa said 79-year-old Ron Smith, a lifelong fan of the Birmingham side, had been suffering from COVID-19 for four weeks.
"The Aston Villa family are saddened to announce that Ron Smith, the father of our current head coach Dean, has passed away at the age of 79," said a club statement.
"Ron, who had recently been living in a care home after being diagnosed with dementia six years ago, contracted coronavirus four weeks ago and after a short spell in hospital passed away with his family at his side.
"A lifelong supporter, Ron was a steward at Villa Park for many years and passed on his love of the club down to his children.
"As well as being a regular at home games, Ron was also there to witness that greatest of days in May 1982 when Villa lifted the European Cup in Rotterdam.
"The thoughts of everyone at the football club are currently with Dean and his family at this most distressing of times and we would kindly ask for the family's privacy to be respected."
Smith is not the only Premier League boss to lose a close relative to the virus, with COVID-19 also claiming the life of the 82-year-old mother of Manchester City manager Pep Guardiola last month.