The coupons promise free coffee to African American customers.
Images of the coupons are being shared on a website that gained notoriety during the 2016 presidential election.
Starbucks says the coupons are completely false and in no way associated with the company.
The hoax comes amid protests sparked after two black men were arrested for trying to use the bathroom and refusing to leave.
Starbucks CEO Kevin Johnson issued a personal apology to the men.
In late May, the company plans to close all of its 8,000 U.S. stores for part of a day so that employees can go through racial bias training.