Wintergreen Advisers on Monday said Coca-Cola shares were "deeply discounted because of poor management and governance" and said the company's CEO, Muhtar Kent, should be replaced.
The fund called Kent "incapable of leading beverage maker's turnaround," and said his failed acquisitions had cost shareholders some $16.3 billion.
Wintergreen, which has less than a one percent stake in the company, laid out a number of structural issues in Coke's management and estimated that the shares were discounted by between $30 and $38 per share.
Read MoreCoca-Cola warns of currency headwinds
"Coca-Cola has serious problems but we believe they can be fixed. With the right management and a commitment to serving shareholders, we think Coca-Cola can thrive again," said David Winters, CEO of Wintergreen.
A company representative told CNBC that it is well-positioned to capture growth in the dynamic beverage industry.
"We utterly reject David Winters' claims. Once again his statements are without merit and are designed to try to grab some headlines in the absence of any meaningful or factual contribution," the representative said in a statement.
"Muhtar Kent and the company's leadership team have outlined meaningful strategic plans to accelerate sustainable and profitable growth and deliver long-term value to our shareowners."
Coke shares closed about 1 percent lower at $40.57 per share. The stock has gained about 4 percent over the past year, largely under-performing the S&P which gained more than 12 percent over the same period.