The family said the Bradman Foundation failed in its duty to safeguard the batsman's image when it signed an agreement this month allowing Bangalore-based firm Unibic India to market "Bradman Chocolate Chip Cookies".
A statement issued by Bradman's family accused the foundation of cashing in on the image of Bradman, who died in 2001.
"Sir Donald is a loved and missed family member, not a brand name like Mickey Mouse," the family said in a statement on Thursday. "Sir Donald would be adamant in his opposition to his use of his name. So is his family."
The statement said the family had held concerns for some years about the foundation's handling of the Bradman name.
Bradman, a cricketing icon still revered in his homeland and on the subcontinent, is the most successful batman in the game's history, with a Test average of 99.94.
Memorabilia connected to Bradman, who died in his Adelaide home in February 2001 at the age of 92, fetches hundreds of thousands of dollars.
The foundation denied misusing Bradman's name, saying it had been signing commercial licensing agreements using The Don's name for years and after being given the go-ahead by the batsman himself.
"In its operations, the Bradman Foundation has at all times gone to great lengths to preserve the good name and reputation of the person acknowledged as the world's greatest cricketer," the foundation said.
"In 1992, Sir Donald Bradman authorised and encouraged the Bradman Foundation to embark upon a program of commercial use of his name to ensure the financial future and stability of the charitable organisation.
The foundation jealously guards the use of the Bradman name and has taken court action on a number of occasions over unauthorised usage.
In 2000, cricket-mad Prime Minister John Howard changed Australia's corporations law in an unprecedented move to prevent businesses falsely suggesting a connection to Bradman.
The move came after a sex shop attempted to register the name "Erotica on Bradman" in the cricketer's hometown of Adelaide.