Nestlé, which cut its sales outlook earlier this year, acquired the stake in Givaudan 11 years ago as part of a deal to sell Givaudan its food ingredient company FIS.
"Nestlé has been very satisfied with its holding but believes now is the appropriate time to divest," said the firm.
Nestlé owns 926,562 shares in Givaudan and is selling them via an institutional private placement managed by Goldman Sachs.
The sale is expected to raise more than $1bn, money that could be used for bolt-on acquisitions or a share buyback, said analysts.
We're talking surgery, not amputation
Nestlé has been clear about its intentions to divest under-performing brands and businesses, with CEO Paul Bulcke recently telling investors he had drawn up lists of businesses that could be fixed and those that could not.
The company - which recently sold the bulk of its Jenny Craig weight-loss business - has not commented on speculation that it is also seeking a buyer for its Powerbar brand, but Bulcke told investors in October that several businesses had been "sailing under the radar screen for too long without being part of the party”.
In an interview with Bloomberg in August about how Nestlé might go about deciding which brands to prune, Thomas Russo, a partner at Gardner Russo & Gardner and a Nestle investor since 1987, said: “We’re talking surgery, not amputation.
"They allocate capital to businesses with high-return prospects, and you would think that those starved of capital would end up being potentially available for sale. I would support that.”
For each under-performing business, “you bring it into acceptable terms and you have a timeline for that, or you sell it off,” Nestlé CEO Paul Bulcke told investors in March.
Nestlé has blamed a deceleration in emerging markets, lackluster sales in Europe and poor performances from diet products, water and frozen entrees for its recent weak performance.