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 More Coca-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.
Coke shares were last down about one percent in midday trading. Coke did not immediately respond to CNBC's request for comment.