"Bayer needs a new strategic positioning, which cannot be credibly accomplished under Werner Baumann," Ingo Speich, head of sustainability and corporate governance at Deka, told the Frankfurter Allgemeine Sonntagszeitung (FAS) newspaper in remarks published on Saturday.
The mutual funds firm is among Bayer's 20 largest shareholders.
"There is a window of opportunity for Chairman Norbert Winkeljohann to act before the annual general meeting at the end of April. He has to seize that opportunity, otherwise the pressure on him will increase as well," Speich added.
He said a successor would have to come from outside the company.
"Generally speaking we are always open to a constructive dialogue with our stakeholders," a Bayer spokesperson said, declining to comment specifically on the interview.
Despite recent improvements in the company's agriculture business and drug development prospects, Bayer shares have been weighed down by litigation over glyphosate-based herbicide Roundup and over environmental pollution related to chemicals known as PCBs.
The legal claims are legacy issues from its takeover of Monsanto for more than $60 billion in 2018.
Baumann, who engineered the troubled Monsanto deal, was given a new contract in 2020 that runs until 2024 and said at the time he would leave the company when that term expires.
A week ago mutual funds group Union Investment criticised Bayer's chair for a lack of engagement, such as exploring a spin-off of the company's consumer health division.
Bayer is also facing demands from activist investor Bluebell Capital Partners to break up the company, including selling off its consumer health unit and later a separation of its pharmaceuticals and agricultural businesses.
Another activist investment fund, hedge fund veteran Jeffrey Ubben's Inclusive Capital Partners, said this month it had also acquired a stake in Bayer.
(Reporting by Ludwig Burger; editing by Jason Neely)