This paper aims to investigate the hydrothermal and entropy generation characteristics of a non-Newtonian nanofluid containing CuO nanoparticles in an offset strip-fin microchannel heat sink (MCHS). The base fluid is solution of 0.5 wt% Carboxymethyl Cellulose (CMC) in water. This study investigates the effects of nanoparticles concentration, Reynolds number and geometric size of strip-fin on the performance of MCHS from the viewpoint of both the first and the second thermodynamic law. The results reveal that enhancing the Reynolds number improves the performance of MCHS by boosting the convective heat transfer coefficient of the working fluid which favourably reduces the CPU surface temperature and thermal entropy generation rate and importantly leads to the temperature uniformity of the CPU surface. However, increase in Reynolds number adversely affects both the pumping power and the frictional entropy generation in the system. Therefore, the optimal strip-fin size is investigated to find the optimum performance of the offset strip-fins MCHS from the viewpoint of both the first and the second thermodynamic law. The optimal results show that the highest ratio of heat transfer enhance- ment to pressure drop increment, using the nanofluid instead of base fluid, is 2.29. In addition in the optimal case, the minimum total entropy generation rate of the nanofluid is 2.7% less than the base fluid.