In this article, we present a model of Physics-informed Neural Networks (PINNs) for predicting the anisotropic hyperelastic behavior of the human passive myocardium. PINNs adhere to the governing equations and the boundary conditions by integrating physical laws into the neural network architecture. They are used for forward and inverse simulations under non-standard, complex geometries and loading conditions. The first example features a plane strain shear test, a common protocol in soft tissue mechanics, where we provide a comprehensive comparison of three different total loss functions—namely, the minimization of the PDEs, the total potential energy, or a combination of both—for forward problems as a surrogate to finite element analysis (FEA). The second example deals with a patient-specific geometry of basal myocardium—obtained from cardiac magnetic resonance imaging—for forward and inverse analyses. Key findings reveal that apart from the accurately predicted primary fields, that is, displacements, the inverse design also provides a true estimate of the anisotropic material parameters from ground truth data obtained from experiments or FEA. Limitations remain in the performance of PINNs for forward simulations of the 2D basal myocardium, particularly with respect to computational demands and sensitivity to network architecture and hyperparameters. Despite challenges in accurately predicting secondary fields, for example, stresses, PINNs demonstrate their potential for inverse simulations, particularly in identifying anisotropic constitutive parameters that can be used in the case of noisy or incomplete datasets in future biomechanical applications.