The ex-Ireland international, who won 26 caps, had been living with dementia since 2015 and finished his managerial career in 2009 with Newcastle United.
"We are sad to announce that Joe passed away peacefully this afternoon surrounded by his family," said the statement reported by the BBC.
He retired at 30 the following year after a knee injury.
Kinnear had short spells in charge of India and Nepal and then managed Wimbledon from 1992 to 1999 before stints at Luton Town, Nottingham Forest and Newcastle United.
Tottenham manager Ange Postecoglou described Kinnear as "one of these figures that will always be remembered at this football club for his achievements".
Kinnear "was a distinguished manager and outstanding player. All our love and support goes out to his family and friends," he added after Spurs' win over Nottingham Forest on Sunday.
