The tech giant's status page showed the App Store, iTunes, iBooks store and Mac App store went down from 0900 GMT and were offline until around 2030 GMT.
Similar outages were seen in Apple online services in Britain and France. The Next Web, an international technology news site, said it had reports of outages affecting more than 40 countries.
"We apologize to our customers experiencing problems with iTunes and other services this morning," Apple said in a statement emailed to AFP, blaming an internal domain name system error, referring to the system which locates Internet addresses.
"We're working to make all of the services available to customers as soon as possible, and we thank everyone for their patience."
Apple's iCloud and mail services were also down, but appeared to have been restored after around four hours, according to the status page.
Other services such as FaceTime, messaging and Apple TV did not appear to be affected.
The outage made it impossible for iPhone and iPad users to download music or to install or update apps on their devices.
Apple support forums included complaints from users around the world, including the Netherlands and Iceland, unable to install or update apps.
Reddit forums mentioned problems from users in Britain, Australia and elsewhere.
The news comes two days after Apple announced details about its smartwatch, which will be available in several markets on April 24, along with a new MacBook computer.
Apple said at the event that it has sold more than 700 million iPhones since launching the device in 2007.
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