The prophetic experience pushes a person to the absolute edge of their physical and mental limits. As Daniel listens to the spoken words, he is actually absorbing the intense spiritual energy radiating from the figure revealed to him [יוסף אבן יחיא]. This overwhelming encounter immediately causes him to fall into a deep sleep.
The reason for this sudden collapse is explained in a few ways. The heavy slumber may be driven by an immense fear that overtakes him [רש״י, מצודת דוד], or it might be the result of extreme physical exhaustion [יוסף אבן יחיא]. Alternatively, the very act of hearing the voice deepens Daniel's physical weakness, pulling him down into a unique prophetic trance [מלבי״ם]. Regardless of the exact cause, this state is defined as a complete loss of consciousness [ביאור שטיינזלץ]. Utterly drained, Daniel is left lying completely flat, with his face pressed directly against the earth [מצודת דוד, ביאור שטיינזלץ].