Given the effect of urbanization on land use and the allocation and implementation of urban green spaces, this paper attempts to analyze the distribution and accessibility of public parks in India’s Bengaluru city (previously known as Bangalore). Availability, accessibility, and utilization—the key measures of Urban Green Spaces (UGS)—are mostly used in health research and policy and are important components of Planetary Health Equity in the context of studying UGSs and health. A geo-spatial method was used for mapping the park’s distribution and measuring its accessibility, using road network data. To understand equitable access to the parks, four socio-economic parameters—population density, the percentage of the population below 6 years of age, the proxy wealth index, and scheduled caste population—were correlated with the parks’ accessibility. This spatial distribution revealed that 19 of 198 wards did not have a single park and that 36 wards only had one park. About 25–29% of wards did not have accessibility to neighborhood-level and community-level parks within a 400–800 m distance. These parks must be accessible within a walking distance of 400–800 m but were found to most likely be inaccessible on the periphery of the city where the population density is low and the children population is high, in comparison to the central part of the city. Similarly, parks were found to be inaccessible in the eastern part of the city where the scheduled caste population is high and also found to be inaccessible for the low-income neighborhoods residing in the western part and southern periphery of the city, indicating the uneven distribution of and inequitable access to public parks. Our study proposes a reshaping of both neighborhood parks and community parks in an attempt to look beyond biodiversity, through the planetary health equity approach, by noting that, while biodiversity indirectly has a positive effect on health, public parks should not only be considered as advancing environmental sustainability and climate resilience, but also as improving the health and wellbeing of the population. Affirmative action in terms of the availability of public parks with adequate area requirements and essential services at a neighborhood scale is required to redress the inequity of access; in addition, the accessibility of parks must be considered important during urban planning.