On its website for sellers, Amazon said items it was still accepting include groceries, baby products, pet supplies, health and household products and personal care items like shampoo. Amazon will still ship nonessential items to customers if it already has the products on the shelves in its warehouses.

“This is the responsible thing for Amazon to do, to make sure that those essentials are checked in first, and it is impossible to do that if you have millions of other shipments,” said Fahim Naim, a former Amazon employee who now runs eShopportunity, an e-commerce consultancy focused on Amazon.

As Americans hunker down, they have been turning to Amazon in droves to bring products to their doorsteps, not just for toilet paper and hand sanitizer but for all kinds of items, from condoms to puzzles for children.

With sales up, brands have been scrambling to restock Amazon’s warehouses, which has had trouble processing so many products at once. Its loading docks to bring shipments into its warehouses have turned into a major choke point in American e-commerce.

Amazon not only must manage its own demand, but it depends on a work force that lives amid the outbreak. “Amazon is having a double whammy,” said Guru Hariharan, a former Amazon employee whose company, CommerceIQ, advises large brands on their Amazon business. “The warehouse staff is reducing but at the same time orders are increasing.”