“We have the power and tools to do something about this. We have thousands of stores which, from an economic perspective, can make an impact,” said Rabyaah Althaibani, a Yemeni-American organizer and member of YAMA.

The Post declined to comment on the criticism of the cover and the boycott, including whether it has had an impact on sales of the newspaper.

The Post cover said, “Here’s your something. 2,977 people dead by terrorism,” a gibe at Ms. Omar, a Minnesota Democrat, in response to a comment that she made about the Sept. 11 attacks that her supporters have said was misconstrued.

The Yemeni-American bodega owners expressed concern that the provocative imagery of the World Trade Centers in flames could trigger violence against Muslims in New York — a fear they say has been more pronounced in the community since Mr. Trump was elected.

“They are propagating hate and they don’t care what the outcome is, they don't realize the magnitude of the hate they are spreading,” said Husam Kaid, 19, who works part time at his family’s bodega in Midtown.

Still, the Yemeni-American bodega owners are not united over using their economic power to boycott The Post.

Some said they were concerned that Yemeni-Americans could face repercussions for becoming the face of protest against a conservative news outlet owned by Rupert Murdoch.