The issue, which impacted the Prime Video app on iOS and tvOS devices, has been resolved and the app is now available for download in the app store, an Amazon spokesperson said.
Other Amazon apps, including its shopping app and Amazon Music, remained unaffected.
The Prime Video app has seen 5 million downloads in September alone, according to app data website Sensor Tower.
Apple did not respond to a Reuters request for comment.
Reporting by Neha Malara in Bengaluru; Editing by Anil D'Silva and Shailesh Kuber