The biomechanical properties of cells and tissues play an important role in our fundamental understanding of the structures and functions of biological systems at both the cellular and subcellular levels. Recently, Brillouin microscopy, which offers a label-free spectroscopic means of assessing viscoelastic properties in vivo, has emerged as a powerful way to interrogate those properties on a microscopic level in living tissues. However, susceptibility to photodamage and photobleaching, particularly when high-intensity laser beams are used to induce Brillouin scattering, poses a significant challenge. This article introduces a transformative approach designed to mitigate photodamage in biological and biomedical studies, enabling nondestructive, label-free assessments of mechanical properties in live biological samples. By leveraging quantum-light-enhanced stimulated Brillouin scattering (SBS) imaging contrast, the signal-to-noise ratio is significantly elevated, thereby increasing sample viability and extending interrogation times without compromising the integrity of living samples. The tangible impact of this methodology is evidenced by a notable three-fold increase in sample viability observed after subjecting the samples to three hours of continuous squeezed-light illumination, surpassing the traditional coherent light-based approaches. The quantum-enhanced SBS imaging holds promise across diverse fields, such as cancer biology and neuroscience where preserving sample vitality is of paramount significance. By mitigating concerns regarding photodamage and photobleaching associated with high-intensity lasers, this technological breakthrough expands our horizons for exploring the mechanical properties of live biological systems, paving the way for an era of research and clinical applications.