Detach debugger in Android Studio

The answer is the Close button. As of Android Studio v3.4 it's a red square block icon (previously was a red X).

It turns out I couldn't see it because it was hidden under the more >> icon.

I'm writing this assuming that Android Studio uses the same convention as IntelliJ IDEA.

Click "close" (the button with the red ✕ in the debug panel):

You will be prompted. Choose whether to disconnect and/or terminate: