Third Point, which owns 7 percent of Campbell's stock, fired back hours later, accusing the heirs of trying to frighten smaller shareholders by suggesting that the outcome of a vote next month has been decided before it even takes place.
Campbell said Bennett Dorrance, Mary Alice Malone, Archbold van Beuren, Charlotte Weber and some other family members - who own a combined 41 percent stake in the company - plan to vote in favor of its existing board at a shareholder's meeting on Nov. 29.
This suggests it could be very difficult for Third Point, run by billionaire activist investor Daniel Loeb, to win board seats.
"This group of billionaire heirs and heiresses are attempting to intimidate smaller shareholders by flaunting their inherited voting bloc as an impenetrable moat," Third Point said in a statement.
Given that Dorrance, Malone and van Beuren serve on Campbell's board, it was widely expected that they would clash with Loeb's campaign, which alleges that the company has been mismanaged for years.
Shares in Campbell were down 3.9 percent in morning trading. Third Point said the drop suggested shareholders were unhappy with these heirs' decision to back the current board.
The $18 billion hedge fund proposes replacing all directors with a 12 person-slate that includes George Strawbridge, another descendant of John Dorrance, who invented condensed soup and ran Campbell nearly a century ago.
Former Hostess Brands CEO William Toler and Third Point partner Munib Islam as well as marketing experts have also been nominated.
Each side is now fighting for shareholders' votes.
Campbell has said it does not endorse any of Third Point's nominees and is urging investors to re-elect its entire board, while Loeb is blaming the board for the stock's underperformance and is urging investors to back him.
The 149-year-old company, which revolutionized the home-cooking industry with easy-to-prepare soups and low-cost production techniques, has been struggling to attract young consumers to its namesake soups and Pepperidge Farm cookies.
(Reporting by Richa Naidu and Svea Herbst-Bayliss; Editing by Frances Kerry)