Cuprous oxide nanoclusters, microcubes and microparticles were successfully synthesized by a simple co-precipitation method. Phase purity and crystallinity of the samples were studied by using X-ray powder diffraction. Transmission electron microscopy (TEM) images show different morphologies like nanoclusters, microcubes and microparticles. For linear and nonlinear optical measurements, the as-synthesized Cu₂O with different morphologies were dispersed in isopropanol solution. The absorption spectrum recorded in the visible regions shows peaks that depend on the morphology of the particles and the peak shifts towards red region as one goes from nanoclusters to microparticles. Simple open-aperture Z-scan technique is used to measure nonlinear optical properties of cuprous oxide at 532 nm, 30 ps excitation at 10 Hz repetition rate. Cuprous oxide nanoclusters show reverse saturable absorption (RSA) behaviour, the microcubes and microparticles at a similar concentration exhibit saturable absorption (SA) type of behaviour at lower peak intensities and exhibit RSA within SA at higher peak intensities. The results show that the transition from SA to RSA can be ascribed to the two-photon absorption (TPA) process.