Step 1: A continuous variable can take any value within an interval on a continuous measurement scale, with no minimum gap between two possible values.
Step 2: Kilogram measures weight, minute measures time, and centimeter measures length, all of which are physical quantities that vary continuously and can be measured to any degree of precision.
Step 3: Rupee measures monetary value, which is expressed in fixed discrete denominations (whole rupees and paise); money amounts are counted in indivisible smallest units rather than measured on a continuous scale.
Step 4: Hence Rupee is the unit that does not measure a continuous variable.
Final answer: \(\boxed{\text{Rupee}}\)