His daughter Ciara Dee (19) and Celtic player Catherine Fleming (27) were also in the car but were not badly injured.
Mr Dee was rushed to Mayo General Hospital after the crash at Williamstown in Co Galway at 9.15am yesterday.
Ciara wrote on her dad's Facebook page: "Can't believe this day. Love you to bits Dad, always will."
FAI chief executive John Delaney said: "I am deeply saddened at this tragic loss.
"I had enormous personal regard for Jeremy's wide-ranging contribution to the Irish football family. I take this opportunity to offer my sincere condolences to his family," he added.
Jeremy was a coach and development officer for more than 10 years.
The Women's National League game was called off after news of the tragedy became known.
"Our thoughts and prayers remain with those involved at this time," a statement said.
Mr Dee's death was one of three road fatalities over the weekend.
Gardai in Galway are searching for an alleged hit-and-run driver after Gerry Keane (65) was killed after being struck by a car which left the scene.
Mr Keane, from Ardrahan, Co Galway, was walking in the local village when hit by the dark coloured car at around 7.30pm on Friday.
And in Co Clare last night a woman in her 20s was pronounced dead after the car in which she was travelling with another woman crashed on the northbound lane of the N18 at Barefield.
The accident happened at 4pm close to Ennis.