The wholly-owned Indian subsidiary of the Atlanta-based company has asked well-known photographer Sharad Haksar to remove the billboard and make an unconditional apology or face a legal suit and damages claim of two million rupees ($46,000).
The billboard, which is seven metres by nine metres, shows a row of plastic pots under a dry hand pump, a common scene in Indian villages and towns, where water is scarce.
In the background is the familiar Coke logo with the tagline, 'Drink Coca-Cola.'
"It's an infringement of our trademark, but we respect Haksar's right to creative expression and have been in discussions with him," said a Coke spokesman.
"We hope to settle the issue amicably," he said.
Haksar, who rents a billboard on a busy arterial road in the southern city of Chennai to showcase his work by often highlighting a social issue, said he would not remove the billboard and will go to court, if necessary.
"I am not going to apologise as I haven't done anything wrong. It's my visual interpretation of the water shortage in Madras," said Haksar, who has worked on advertisement campaigns for Coke and plans a book on international brands in ironic Indian situations.
"They are my client, why would I do anything to hurt them?" he said.
"We appreciate Haksar's efforts and condemn Coca-Cola's attempts to silence a public discourse on the issues"
India Resource Centre
Several local environmental groups and activists have jumped on the spat as further evidence of the growing opposition to the manufacturing and trade practices of the world's biggest soft drinks maker in India.
"Haksar's billboard highlights the severe water shortages being experienced by communities that live around Coca-Cola's bottling plants across India," said a release from India Resource Centre.
"We appreciate Haksar's efforts and condemn Coca-Cola's attempts to silence a public discourse on the issues."
Haksar said he did not know about the opposition to Coke's manufacturing practices, which activists and environmental groups claim is causing a severe depletion of the water table in the areas where the bottling plants operate.
India accounts for less than 1% of Coke's global sales but is considered an important emerging market.