The unexpected decision to replace Schumacher with finance chief Fernando Fernandez stemmed from the belief that Fernandez was best suited to drive the company's turnaround strategy, the source indicated.
Schumacher was taken aback by the decision, but the source noted that there was "nothing untoward" about the process.
He did not respond immediately to Reuters' request for comments via LinkedIn.
Peltz, the founder of U.S. hedge fund Trian Fund Management, joined the Unilever board in May 2022, having previously served on the boards of Procter & Gamble and Mondelez.
Unlike some activist investors, Peltz emphasizes a collaborative approach with companies, yet he has been urging Unilever for years to revitalize its operations.
When Schumacher, a Dutch executive, was appointed CEO of Unilever in January 2023, Peltz expressed strong support for the decision.
Peltz and Schumacher previously worked together at H.J. Heinz, where Peltz joined the board in 2006, and Peltz's firm appointed two additional directors to the Heinz board.
Schumacher's abrupt exit after less than two years in the role impacted Unilever's stock, which dropped by as much as 3.4% on Tuesday, despite having risen over 9% since Schumacher took over on July 1, 2023.