A thread clamping device for a spindle for detachably securing a thread in a clamping gap, comprising a first clamping unit with an inner casing that can be arranged coaxially to the spindle, a thread separator that can be secured in an axial direction on the inner casing, the first clamping unit being securable on an upper part of the spindle for axial positioning, and a second clamping unit having a clamping element that can be adjusted axially relative to the first clamping unit between a clamping position closing the clamping gap between the thread separator and the clamping element and an open position opening the clamping gap. The thread separator is designed to be secured on the spindle upper part for axial positioning and to be rotationally coupled to the spindle upper part, and the thread separator and the inner casing can be rotationally coupled to one another.