The outage, which began just before 5 a.m. EDT, also hit iCloud account and sign in, as well as iCloud Mail, though service seems to have been restored to both of those. In a comment to iMore, an Apple spokesperson says that the company is working to fix the problem, which was caused by a DNS error.
We apologize to our customers experiencing problems with iTunes and other services this morning. The cause was an internal DNS error at Apple. We're working to make all of the services available to customers as soon as possible, and we thank everyone for their patience.
The disruption, which Apple says currently affects all users, prevents people from downloading or purchasing content from the iTunes Store, App Store, iBooks Store, and Mac App Store.