Luger Nodar Kumaritashvili was killed on February 12 when he was catapulted off the track and crashed into steel pillars during a training run at the Olympic sliding centre hours before the opening of the Games.
An FIL report absolved organisers of the blame for 21-year-old Kumaritashvili's death and the Olympic competitions went ahead, though the start was lowered and a wall was built to cover the pillars.
"According to information from the president of the Luge Federation of Georgia, the family is in urgent need of financial support," the FIL said.
"Some years ago their house was completely destroyed by fire. Mainly with the help of their only son, the family had begun to rebuild the house which is still far from completion," it said.
The FIL said it had launched a donation campaign and opened a bank account.
"As immediate support, the FIL already transferred 10,000 euros to the family," it said.
An FIL official told Reuters all 53 national luge federations had been contacted.
Several investigations into the crash are still ongoing.
The International Olympic Committee, also awaiting the final reports, has said it had a moral responsibility but not a legal one, with the federation and organisers responsible for the construction of the track and the staging of competitions.