Microsoft has resolved the issues.

As per their status page, Microsoft is applying network configuration changes and performing failovers to improve the situation.
We experience some improvement ourselves however not all monitors have recovered yet.
We continue to monitor the situation.

Microsoft has expanded the scope of the issue which is now affecting all regions worldwide: https://azure.status.microsoft/en-us/status

We continue to monitor the issue.

Microsoft Azure is experiencing connectivity issues.
As they are our principal infrastructure provider this impacts our services.