The June 2013 802.11ac model of the Extreme now officially support this.
From "Choosing a backup drive" in Apple's Mac Basics: Time Machine backs up your Mac:
Time Machine can only back up to a external drive connected to an AirPort Extreme 802.11ac base station. Time Machine cannot back up data to external drives connected to other AirPort Extreme base station models.
And the printed manual states:
Using Time Machine with Your AirPort Extreme
If you connect a USB hard disk to your AirPort Extreme, you can use the Time Machine
application to back up all your Mac computers, including your photos, music, movies,
After you set up Time Machine, it automatically backs up your computer on a regular basis.
Use Time Machine preferences to set up automatic backups, use a different backup disk, or
adjust other settings.
To set up or adjust Time Machine on a computer using Mac OS X v10.5.7 or later:
- Choose Apple > System Preferences, and then click Time Machine.
- Slide the switch to ON.
- Click Select Disk.
- Choose your AirPort Extreme and click Use Disk.
(For those in doubt of replacing an Express with an Extreme: note that the latter does not support AirPlay! I noticed that just in time...)