The museum said it had two employees who have showed symptoms of the virus. One is awaiting a test; the other is at home. The museum — which made its decision in consultation with the mayor’s office — also said it has been preparing for this possibility for several weeks, and is implementing an operational plan, which includes provisions to support salaried and hourly staff.

“While we don’t have any confirmed cases connected to the museum, we believe that we must do all that we can to ensure a safe and healthy environment for our community, which at this time calls for us to minimize gatherings while maintaining the cleanest environment possible,” Mr. Weiss said.

Even before they made the announcement to shut down, many arts organizations were scrambling to navigate President Trump’s ban on travel from Europe, which threatened to leave many without some of their most important artists and biggest stars.

The music director of the New York Philharmonic, Jaap van Zweden, is currently in his native Amsterdam, and orchestra officials were girding themselves for the possibility that he could be stranded there. The Metropolitan Opera faced the loss of some of its leading stars, including Anna Netrebko, who was supposed to sing there later this month. And the Rotterdam Philharmonic noted the ban as it postponed a tour marking the 50th anniversary of its first United States trip.

Governor Cuomo’s limit on large gatherings effectively closed Broadway theaters. Lincoln Center said that its constituent organizations would stop performing as of Thursday evening. The Chamber Music Society of Lincoln Center said that its musicians would play their planned performances on Thursday and Sunday without an audience, and the concerts will be streamed at chambermusicsociety.org.