Just by chance I just discovered a workaround:
The DNS Hostname of our Zimbraserver is de-dd-srv-1101.domain.net. For our users we have a DNS cname Record zimbra.otherdomain.com resolving to the same IP as de-dd-srv-1101.domain.net.
Logging in to the Admin Console via zimbra.otherdomain.com is working fine.
Logging in to the Admin Console via de-dd-srv-1101.domain.net does not work. (I tried this all the time since this was what we used to do since ZCS 3.x)
The Zimbra Web Client is working with both URL's as it did before the upgrade.
DNS & MX Records weren't changed.