He and one of his Twitter followers each plan to live for a week on the monetary equivalent of food stamps or less.
The mayor's week starts Tuesday. The North Carolina woman's began Sunday.
The mayor prepared for the challenge with a grocery purchase of $27.98.
Booker tweeted a picture of a receipt of the purchases he made Saturday at a Pathmark store in neighboring Irvington. The vegetarian mayor's grocery list included pink and black beans, corn and red delicious apples.
Booker declined requests Monday to be interviewed. He is using social media to provide updates.
Other city officials around the country have taken part in similar challenges, including Philadelphia Mayor Michael Nutter this past April.