Hodgkiss, whose death was announced by the Old Trafford club on Monday, served the Red Rose with distinction for more than two decades, as board member, treasurer and vice-chairman before he succeeded Michael Cairns in 2017.
The county have not given a cause of death but a spokesman confirmed to the PA news agency that it was “coronavirus-related”.
“It is with great sadness that Lancashire Cricket announces the passing of its chairman David Hodgkiss OBE,” read a statement.
“He was much loved by everyone at Lancashire Cricket Club and respected throughout the cricketing world. Our sincere condolences and thoughts and prayers are with his family.
“A further statement will be released in due course but at this time we ask that everybody respects the family’s privacy.”
England and Wales Cricket Board chairman Colin Graves paid tribute to Hodgkiss.
Graves told the BBC: “He was a vital part of cricket in Lancashire and was passionate about growing and developing the sport in the county.”