The stake, which analysts estimate is worth about 500 million euros, is what remains after Danone sold most of its 21.29% stake in 2018. Danone is still Yakult's largest shareholder.
Existing commercial partnerships, including joint ventures in India and Vietnam, will remain in place.
"We see this as a positive and shareholder-friendly move by Danone," said Jefferies analysts in a note.
Barclays analysts said the sale would help Danone focus expansion of plant-based dairy in Europe and Americas behind its key brands Alpro and Silk, while helping deleverage its balance sheet.
Barclays also said Danone should launch a strategic review of its bottled water business, like rival Nestle has, pointing out that the COVID-19 pandemic has hurt sales and profits of a business that was already underperforming.
"Given high investment needs, especially in packaging ... we think a solution is needed for the division to be able to grow in a profitable manner," Barclays said.
Danone declined to comment on whether it would consider options for its water business.
Danone shares were down 0.5% in Paris.
(Reporting by Martinne Geller; editing by Jason Neely)