Viscoelastic characterization of biological tissue has significant biomedical value. In this study, we propose a wavelet-based photoacoustic viscoelastographic microscopy to characterize the viscoelasticity of tissues beneath the optical scattering depth from photoacoustic oscillation signals. Irradiated by laser pulses, biological tissue absorbs energy, expands, continues oscillating, and emits damped transient ultrasonic waves, i.e., photoacoustic oscillation signals, for a short time. A damped oscillation wavelet is applied to map photoacoustic oscillation signals into a representation of time, frequency, and decay rate. We can evaluate the frequency and decay rate of the photoacoustic oscillation signals. By considering the interrelationships among frequency, decay rate, shear modulus, and shear viscosity coefficient, we can generate images that depict the shear modulus image and shear viscosity coefficient image within the tissue. These images of the shear modulus and shear viscosity coefficient collectively form the viscoelastogram of the tissue, offering a comprehensive portrayal of its viscoelastic properties. Our study has potential biomedical value and may improve the accurate diagnosis of diseases and achieve more effective early interventions.