Yes, it is permanently installed. That made me uneasy at first, but I've had it for almost half a year now and haven't had any problems with it. My hygienic concerns didn't last long either, because all the water is used up with each pass (so you just fill up as much as you need before each pass).

The water tank is fixed and NOT removable.

Supplementary remark:
Since this machine has its own jug (unlike capsule machines or fully automatic machines, where you place the individual cup underneath), you usually use this jug to fill the water tank. The jug also has a scale, so filling it is easy and does not require any additional dishes.