But there will be strict rules for customers, including the wearing of a face mask. If customers don't have their own, one will be provided.
Visitors will also be asked a set of health questions at the door and have their temperature checked.
There will be a reduced number of customers in the store and deep cleans will happen throughout the day.
About 100 Apple stores have already reopened worldwide.
In a post detailing how the new measures would apply in the US, Apple said: "When a store in your area does take this step to reopen... things may look and feel a little different.
"For one thing, you'll find yourself with plenty of space."
One-on-one help at its so-called genius bars will still be provided, at a suitable distance.
Apple will also allow customers to collect goods from outside, in order to limit the number of in-store visitors.
In the UK, some garden centres and DIY stores have been allowed to reopen - but the government has not yet said when High Street shops can start trading again.