"Shopping" is a noun here, not a verb. It's the name of a regular domestic task, meaning that you need to go and buy some household basics : bread, milk, toilet paper, and so on. Grammatically, it's the same as "doing the laundry" : do + the + name of chore.
This is different from "go shopping", which might also be a recreational or social activity, such as looking round fashion shops.
Note that the 'ing' form can have many grammatical functions:
I am shopping = present participle
I like shopping = gerund
I do the shopping = (verbal) noun