This paper analyzes the thermal and hydraulic performance of a counterflow microchannel heat exchanger (CFMCHE) with and without nanofluid as working fluid. A 3D conjugate heat transfer simulation is carried out using a finite volume approach to evaluate the effects of inlet Reynolds number, Brownian motion, and volume fraction of nanoparticles on the pumping power, effectiveness, and performance index of CFMCHE. The accuracy of the code has been verified by comparing the results with those available in the literature. A single phase approach is used for the nanofluid modeling. The base fluid used in the analyses as a basis for comparison was pure water. Two types of nanofluids, namely, water- with a mean diameter of 47 nm and water-CuO with a mean diameter of 29 nm, each one with three different volume fractions, are utilized. In addition, two temperature dependent models for the thermal conductivity and viscosity of nanofluids that account for the fundamental role of Brownian motion are used. Calculated results demonstrate that the effectiveness and performance index of CFMCHE decrease with increasing Reynolds number. Moreover, it is observed that the relative enhancements in the pumping power become more prominent for higher values of Reynolds numbers. It was also found that the performance index and pumping power are not sensitive to volume fraction at higher and lower Reynolds numbers, respectively.