A statement from the museum said the decision to shut its doors from Tuesday night was made to protect staff and visitors during “exceptional times”.
It added more information will be given in the coming days.
“Following official guidance, V&A Dundee will close from tonight,” the statement said. “During these exceptional times, the health and safety of our visitors and staff is our number one priority.
“We will continue to monitor the situation closely and look forward to welcoming visitors back to V&A Dundee as soon as we are able.
“Further information will be available on our website over the coming days.”