Lucas A. Ferrara, an adjunct professor at New York Law School and co-author of the multivolume book “Landlord and Tenant Practice in New York,” said a potential tenant might be able to fight the meat ban if, for example, they showed they had a medical condition that required some sort of “reasonable accommodation” on the landlord’s part.

“Absent an exception of that type,” Mr. Ferrara wrote, “the restriction would otherwise be permissible.”

The listing that mentioned the rule, on nextdoor.com, was taken down on Friday, the day after it was posted, but Douglas Elliman still lists the apartments on its own site, though without mention of the meat policy. The listings do note, “Cats welcome on a case-by-case basis (only one, please).”

One curious couple who did not know about the meat rule balked when they heard about it.

“Oh, we don’t fulfill those requirements,” said the woman, Tessa Ruben.

Then she and her partner, Darian Ghassemi, thought a little more.

“We order in a lot anyway,” said Ms. Ruben, 29, who works for a nonprofit.

“The terrace looks cool,” said Mr. Ghassemi, 31, who works in sales.

They were not able to get into the building because they didn’t have an appointment to view the apartments. After a little more discussion, they decided this was probably for the best.

“What makes me more nervous than the rule itself,” Ms. Ruben said, “is knowing there’s someone upstairs making sure you follow it.”