A central composite design (CCD) was used for the experimental design and results analysis to obtain the optimal processing parameters (acetic acid concentration, liquid to solid ratio, and stirring speed) for the extraction of pepsin soluble collagen (PSC) from muscles of cultured hybrid catfish of Clarias sp. (Clarias gariepinus × C. macrocephalus). Statistical analysis showed that the linear and quadratic terms of these three independent variables had significant effects on the yield of PSC. There was also an interaction between the ratio of liquid to solid and the stirring speed in affecting the extraction efficiency. Optimal conditions for a higher yield of PSC were an acetic acid concentration of 0.67 M, a liquid to solid ratio of 24.65 ml/g, and the stirring speed of 423.64 rpm. The verification of the optimization showed that the percentage error differences between the experimental and predicted values were in the range of 0.22–4.42%. The experimental values agreed with the predicted values, indicating an excellent fit of the model used and the success of the response surface methodology in modeling the extraction of PSC from the muscles of catfish. The experimental results were also fitted to the power law model and it was proven to be appropriate in describing the kinetics of collagen extraction process.