The manager joked about hanging some of them, the lawsuit claims.
The suit alleges a second white manager refused to remove the symbol of racist lynchings, despite numerous complaints, The New York Post reports.
The 11 men, employed by 180 Connect, a Cablevision Systems Corp. subcontractor, say they are discriminated against on the job and the noose was the last straw.
Supervisor Dave Willie "said he put it there to hang anybody who would pass the gate. I was flabbergasted," worker James Jackson Jr. said. "It's just degrading, disrespectful."
He alleged Willie and another white supervisor, Gary Murdock, also joked about the noose.
Despite complaints, the noose hung over their heads for a week, Jackson said.
The workers' lawyers filed an Equal Employment Opportunity Commission class-action discrimination suit, the Post said.
A spokesman for 180 Connect said the firm did "not tolerate in any manner any kind of discrimination or harassment in our workplaces."