Quantitative phase imaging (QPI) has been proven to be a powerful tool for label-free characterization of biological specimens. However, the imaging speed, largely limited by the image sensor technology, impedes its utility in applications where high-throughput screening and efficient big-data analysis are mandated. We here demonstrate interferometric time-stretch (iTS) microscopy for delivering ultrafast quantitative phase cellular and tissue imaging at an imaging line-scan rate —orders-of-magnitude faster than conventional QPI. Enabling an efficient time-stretch operation in the 1-μm wavelength window, we present an iTS microscope system for practical ultrafast QPI of fixed cells and tissue sections, as well as ultrafast flowing cells (at a flow speed of up to ). To the best of our knowledge, this is the first time that time-stretch imaging could reveal quantitative morphological information of cells and tissues with nanometer precision. As many parameters can be further extracted from the phase and can serve as the intrinsic biomarkers for disease diagnosis, iTS microscopy could find its niche in high-throughput and high-content cellular assays (e.g., imaging flow cytometry) as well as tissue refractometric imaging (e.g., whole-slide imaging for digital pathology).