The hat reads "AMERICA WAS NEVER GREAT" - which is a play on Trump's campaign slogan, "Make America great again."
Someone snapped a photo of the employee wearing the hat at a Home Depot in Staten Island, and shared it online.
The photo went viral on social media.
Hundreds of Trump supporters are now threatening to boycott Home Depot in response.
"This is disgusting," customer Trevor McNulty wrote on Home Depot's Facebook page. "If we do not hear what action was taken against this employee and the manager, I will never step foot in any of their stores again. You've got until Monday HD." The comment has been "liked" 54 times.
Another person wrote, "If this woman is not fired I will never shop at Home Depot again. She represents everything that is wrong with our country!"
Hey @HomeDepot you are OK with this????? What an insult to #Vets and ALL Americans #Vets4Trump #Trump2016 pic.twitter.com/BjM835m4rH
- District?fCriminals (@DistOfCriminals) May 18, 2016
Home Depot has swiftly responded to critics on Twitter and Facebook, saying the hat was inappropriate.
@Bikers4Trump Agree this isn't appropriate & we wouldn't allow it, but the store team didn't see it. This doesn't represent HD's opinion.
- The Home Depot (@HomeDepot) May 18, 2016
"We appreciate and understand the concerns of our loyal customers," he said. "In terms of the message, our associates are not permitted to wear items that reflect political statements. Unfortunately, no one on our management team saw her wearing the hat - otherwise, they would have had her remove it immediately."