It’s an honest-to-God doomsday scenario and the ultimate doomsday-prepper market is a mess.

As the coronavirus pandemic takes hold, investors and bankers are encountering severe shortages of gold bars and coins. Dealers are sold out or closed for the duration. Credit Suisse Group AG, which has minted its own bars since 1856, told clients this week not to bother asking. In London, bankers are chartering private jets and trying to finagle military cargo planes to get their bullion to New York exchanges.

It’s...