Smallest Voltage that a comparator can detect
The smallest voltage difference that a comparator can detect is a moving target: New comparators with increasingly low offset and hysteresis voltages are released by manufacturers from time to time. For instance:


Texas Instruments LMP7300 has a worst-case offset voltage of 0.75 mV, and an adjustable hysteresis down to 1 mV/mV. 
Analog Devices AD790 has a 0.25 mV worst-case offset and hysteresis of 0.5 mV


The question appears to have an ambiguity on desired specifications:  

Setting of reference voltage is essentially independent of the noise margin budget, and dependent on the maximum guaranteed input offset voltage. The reference can go down to the ground rail, or single-digit millivolts above it, in many comparators. 

The acceptable noise margin on the other hand is addressed by the comparator's hysteresis, and as indicated above, this can be fractional milliVolts.

Thus, if one were to surmise from the wording of the question that the application requires comparator functions with a reference at the ground rail (0 Volts) and a noise margin of single-digit millivolts, comparators from many major manufacturers easily meet these criteria, such as the ones listed above.

For more stringent requirement specifications, a low noise preconditioning stage is often used, which may raise the signal bias point and / or provide buffering or amplification of the source signal. The problem then becomes one of minimizing noise in the preconditioning stage.

Nanovolt signals such as in medical equipment are commonly handled using such preconditioning, largely freeing the design from comparator constraints.