Apple has released an update to iOS 11 that resolves this issue.
Additional information concerning this update is available here.
https://support.apple.com/en-ca/HT204204

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Previous Description (2017-09-20 14:31:45):

Microsoft and Apple have both posted notifications concerning the latest update to iOS 11 and the use of the native Mail app (Mail.app). Until the problem is resolved, users who install the update should use the Outlook for iOS client from the App Store, which is not affected by this problem.

Both Microsoft and Apple are working to resolve this issue and will post more information on their websites when the problem is resolved.

The Microsoft notification can be followed here:
https://support.microsoft.com/en-us/help/4043473/you-can-t-send-or-reply-from-outlook-com-office-365-or-exchange-2016-i

The Apple notification can be followed here:
https://support.apple.com/en-us/HT208136