Currently, women have to pay to use public toilets while men can use the services for free.
The campaign, dubbed the “Right to Pee” campaign, is led by 35 non-government organisations (NGOs), and urges women in Mumbai’s civic authority to ensure that the service is free for women.
Women currently make up 50% of Mumbai’s civic authority.
Rahul Gaekward, who heads one of the 35 NGOs in the campaign, has outlined three basic requirements for women.
“They should be allowed to pee for free, the public toilets should provide vending machines with sanitary towels, like men have for condoms, and they should have a changing room in the toilets,” he said.
There is an acute shortage of both public and private toilets in India, and public defecation is common across the country.
A census in March found that half of India’s homes do not have toilets.
The campaign is drawing a strong response from both men and women.
One man who signed the petition told the BBC he wanted better facilities for women in all public toilets in the city.
According to Mr Gaekward, more than 7,000 signatures were collected in the crowded and impoverished Kurla area last week.
A female student who signed the petition in the middle-class Dadar suburb said it was a question of dignity for women.