A motion agreed at a meeting of the London Assembly urged the IOC and national organising committees to consider the environmental, social, ethical and human rights records of companies when awarding high-profile partnership and sponsorship deals.
As well as investigating issues that matter to Londoners, the London Assembly acts as a check and a balance on the Mayor.
Dow is a Worldwide Olympic Partner and paid for the plastic wrap around the Olympic Stadium.
Dow Chemical bought the Union Carbide Chemical Company, owners of the Bhopal pesticide plant in India where the 1984 disaster took place.
Over 3,000 people are believed to have died in the Dec 1984 in Bhopal due to the immediate effects of the tragedy.
Assembly member Navin Shah, who proposed the motion, said, "Almost 30 years after the horrific Bhopal chemical disaster, the factory site has still not been cleared up and the survivors and their families continue to fight for compensation."
"It is time for London Organising Committee of the Olympic and Paralympic Games (LOCOG) and the IOC to take their ethical and sustainability code seriously and exclude Dow Chemical from future sponsorship deals," he said.
"It's not too late to clean up their act. We owe it to the victims and their families to demand actions and implement changes to keep out the likes of Dow Chemical from future Games," he added.
Darren Johnson, who seconded the motion, said, "There is a genuine excitement and enthusiasm about the Games across London, but it is in danger of being tarnished by association with companies like Dow Chemical."