Cells are complex living organisms often described as the building blocks of life. The mechanical properties of such cells have been shown to be effective for medical diagnosis. Previous research in this area focus primarily on static methods by identifying local variations in cell elasticity. Atomic force microscopy (AFM) has shown to be effective for such measurements. In this paper we extend on this methodology by developing a dynamic viscoelastic model of the cell, constructed to be well suited for parameter identification. A parameter estimator is then designed for identifying the spatially resolved mechanical properties of the cell. The parameter estimates are shown to converge exponentially fast to the real parameters by employing the provided control input. A key property of this online estimation scheme is allowing for mechanical changes in the cell to be detected over time. Furthermore, the approach can be applied to the problem of identifying the mechanical properties of any elastic material that can be scanned in AFM. A simulation study shows the effectiveness of the methodology.