Nestlé said the shares are being sold not in the open market but through a private placement to institutional investors such as pension funds. Goldman Sachs is arranging the sale.
Nestlé, the maker of KitKat chocolate bars and Nescafé instant coffee, is one of Givaudan's biggest customers for food flavorings. Nestlé acquired its stake when it sold the food ingredient company FIS to Givaudan for a combination of cash and stock in 2002.
"Nestlé has been very satisfied with its holding but believes now is the appropriate time to divest," the company said in a statement.
The sale comes as Nestlé looks to unload underperforming businesses. The company is reviewing its nearly 2,000 business units and has already sold most of its Jenny Craig weight management business for an undisclosed sum.
Nestlé, which is grappling with its slowest annual growth rate since 2009, is streamlining in a bid to focus on specific areas such as infant nutrition. The company's chief eExecutive Paul Bulcke told The Wall Street Journal in October that Nestlé ultimately wants to fix or sell a "sizable percentage" of its underperforming brands and businesses.
Analysts expect Nestlé to sell other assets including its PowerBar fitness bar business, as well as some smaller water brands.
Nestlé holds 926,562 Givaudan shares, a stake valued at 1.145 billion Swiss francs -- $1.28 billion.