Even after the museum reopens to the public, officials expect to see reduced revenue and attendance. As a temporary solution, the Met is exploring whether there is any way it could dip into its $3.6 billion endowment fund.

“No endowed organization that loses its revenue can spend down its endowment without limitation since spending from it today has to be balanced against preserving it to support operations tomorrow,” Mr. Weiss cautioned in an email co-signed by Max Hollein, the museum’s director.

The museum world often looks to the Met for leadership as it did earlier this month when, shortly after the museum decided to close in an effort to help contain the spread of the coronavirus, hundreds of other cultural institutions followed suit. Few museums, though, have the financial resources that the Met does.

“It’s very challenging right now because we don’t have any type of benchmark,” said Seema Rao, deputy director of the Akron Art Museum in Ohio. “We are all watching the Met for guidance and trying to prioritize our staff as best we can. But we are a medium-sized institution going into our third payroll without any revenue, and many of our funders have also taken hits.”

Faced with a shortfall of almost $1 million dollars, Akron has announced that some of its 35-member full time staff would be furloughed, others would be cut back to part-time and department heads would take 10 percent pay cuts. The Carnegie Museums of Pittsburgh have furloughed more than half their 1,003 employees. Last week in Los Angeles, the Hammer Museum laid off 150 part-time student workers. And recently, the Massachusetts Museum of Contemporary Art laid off almost three-quarters of its 165-person staff.