Mechanical forces play crucial roles in tissue growth, patterning and development. To understand the role of mechanical stimuli, biomechanical properties are of great importance, as well as our ability to measure biomechanical properties of developing and engineered tissues. To enable these measurements, a novel non-invasive, micron-scale and high-speed Optical Coherence Elastography (OCE) system has been developed utilizing a titanium: sapphire based spectral-domain Optical Coherence Tomography (OCT) system and a mechanical wave driver. This system provides axial resolution of 3 microns, transverse resolution of 13 microns, and an acquisition rate as high as 25,000 lines per second. External low-frequency vibrations are applied to the samples in the system. Step and sinusoidal steady-state responses are obtained to first characterize the OCE system and then characterize samples. Experimental results of M-mode OCE on silicone phantoms and human breast tissues are obtained, which correspond to biomechanical models developed for this analysis. Quantified results from the OCE system correspond directly with results from an indentation method from a commercial. With micron-scale resolution and a high-speed acquisition rate, our OCE system also has the potential to rapidly measure dynamic 3-D tissue biomechanical properties.