Magnetic resonance elastography (MRE) is a phase contrast-based MRI technology that can create whole brain mechanical property maps in vivo. MRE involves the solution of an inverse problem to estimate mechanical properties. Data noise degrades the accuracy of the recovered property images (elastograms). Most MRE acquisitions aim to achieve signal-to-noise ratio (SNR) above a certain threshold, though low SNR is a common issue. We propose a new method to denoise MRE data through spatiotemporal modeling. By approximating MRE data as low-rank, large improvements in SNR can be achieved, which can lead to the ability to salvage MRE data that otherwise would be unusable.