Microsoft now reports the following:
Current status: We've confirmed that the issue was caused by a routine service update which inadvertently contained a code issue that prevented some users from accessing their mailbox via Outlook on the web. We've reverted the change and have confirmed that service has returned for a majority of affected users. We expect full mitigation within the next 30 minutes.
Root cause: A routine service update inadvertently contained a code issue that prevented some users from accessing their mailbox via Outlook on the web.