Update: this update was initially going to start in September, but the start date has now changed to mid-October.
The .NET Framework 4.7.2 update is scheduled to deploy to Azure App Service apps gradually during October 2018. Currently, these apps are running .NET 4.7.1.
Consider testing your apps locally with the new 4.7.2 version before September. Although breaking changes are not expected, some compatibility issues are possible. Advance testing can be helpful for a smooth transition.
For more information about the release, see the .NET Framework 4.7.2 release announcement. You can also participate in the discussion about the App Service .NET update on GitHub.