In one aspect, a system for monitoring soil composition within a field may include a non-rotating ground-engaging tool configured to be pulled through soil within the field in a manner that performs an agricultural operation on the field. The non-rotating ground-engaging tool may, in turn, define a cavity therein, with the cavity including an opening. Furthermore, the system may include a sensor positioned within the cavity, with the sensor configured emit an output signal through the opening for reflection off of the soil within the field. The sensor may also be configured to detect the reflected output signal as a return signal, with a parameter of the return signal being indicative of a soil composition of the soil within the field.