More than racial composition, it is economic status that will tend to impact the accessibility of supermarkets. However, poverty and heavily minority neighborhoods often go together in inner cities. It is in these places, sometimes referred to as "food deserts" that there are typically very few supermarkets.
Supermarkets tend not to locate in poor neighborhoods in cities. Part of this is an economic calculation about where they can make the most profit. Part of it sometimes has to do with land use laws in cities. One way or another, there tend not to be supermarkets or other stores that have healthy food at decent prices in neighborhoods that are poor and heavily non-white.