Apple - Are Time Machine backups to an external disk attached to a Time Capsule supported?
Yes. You can use Time Machine with a drive connected to a Time Capsule.
This Apple support doc - Backup disks you can use with Time Machine (as of Sept 2015) - says:
Time Machine can back up the data on your Mac to these backup disks:
- An external USB, Thunderbolt, or FireWire drive connected to your Mac
- An AirPort Time Capsule's built-in drive (any model)
- An external USB drive connected to an AirPort Time Capsule (any model) or AirPort Extreme (802.11ac model only)
- Network volumes connected using Apple File Protocol (AFP)
Update: Now Officially Supported
At the time this was written (May 2013), the answer below was correct. Apple introduced new hardware, the Airport ExtremeBase Station (802.11ac) (6th generation) in June of 2013, and backing up to an external drive connected to an AirPort Extreme Base Station (802.11ac) or later AirPort Time Capsule is officially supported. Unfortunately, Apple no longer makes the Time Capsule or AirPort extreme. Also note that while for a long time Apple only supported network backups using AFP (Apple Filing Protocol), they have dropped AFP in favor of current SMB (that is, SMB3) protocols. This support article seems to be getting updates as the support situation evolves.
So, in 2019, your options for wireless backups appear to be a NAS with SMB3 support and advertised Time Machine compatibility or a Mac shared as a Time Machine backup destination (see support article linked above).
Original Answer
It is not officially supported. "Time Machine can’t backup to an external drive that's connected to an AirPort Extreme, Time Capsule, or a drive formatted for Microsoft Windows (NTFS or FAT format). (Click on "Setting up Time Machine backups using an external drive" to reveal the information.)(Update August 2019: the original link now redirects you to current documentation. For historical information, see also Disks that can be used with Time Machine) This is usually because of issues with the network file system not guaranteeing that writes have completed on disk before giving a "success" status.