The application of instrumented indentation allows the identification of conventional material properties such as the elastic modulus and hardness. In the recent past, inverse methods have been developed, by which yield strength, work hardening rates, and tensile strength can be extracted from indentation experiments. However, determining material parameters for cyclic plasticity or fatigue strength still requires laborious and costly conventional fatigue experiments. In the current work, a novel hybrid method is presented that allows identifying material parameters for cyclic plasticity from cyclic indentation experiments by using a model-based inverse identification technique. To validate the method, it is applied to predict the uniaxial stress-strain hysteresis curve only from cyclic indentation results. The first test material has been quenched and tempered 50CrMo4 martensitic steel. The identified material parameters from cyclic indentation experiments predict cyclic uniaxial stress-strain behavior with a high accuracy with respect to the dissipated work per cycle between experimental and predicted values. The transferability of this novel hybrid method has been demonstrated by applying it also to soft technically pure copper, where also very good results have been achieved.