Viscoelastic transformation of tissue drives aberrant cellular functions and is an early biomarker of disease pathogenesis. Tissues scale a range of viscoelastic moduli, from biofluids to bone. Moreover, viscoelastic behavior is governed by the frequency at which tissue is probed, yielding distinct viscous and elastic responses modulated over a wide frequency band. Existing tools do not quantify wideband viscoelastic spectra in tissues, leaving a vast knowledge gap. We present wideband laser speckle rheological microscopy (WB-SHEAR) that reveals elastic and viscous response over sub-megahertz frequencies previously not investigated in tissue. WB-SHEAR uses an optical, noncontact approach to quantify wideband viscoelastic spectra in specimens spanning a range of moduli from low-viscosity fibrin to highly elastic bone. Via laser scanning, micromechanical imaging is enabled to access wideband viscoelastic spectra in heterogeneous tumor specimens with high spatial resolution (25 micrometers). The ability to interrogate the viscoelastic landscape of diverse biospecimens could transform our understanding of mechanobiological processes in various diseases.