We use the Gaia EDR3 to explore the Galactic supernova remnant (SNR) G272.2-3.2, produced by the explosion of a Type Ia supernova (SN Ia) about 7500 yr ago, to search for a surviving companion. From the abundances in the SNR ejecta, G272.2-3.2 is a normal SN Ia. The Gaia parallaxes allow us to select the stars located within the estimated distance range of the SNR, and the Gaia proper motions allow us to study their kinematics. From the Gaia EDR3 photometry, we construct the H-R diagram of the selected sample, which we compare with the theoretical predictions for the evolution of possible star companions of SNe Ia. We can discard several proposed types of companions by combining kinematics and photometry. We can also discard hypervelocity stars. We focus our study on the kinematically most peculiar star, Gaia EDR3 5323900215411075328 (hereafter MV-G272), an 8.9σ outlier in proper motion. It is of M1-M2 stellar type. Its trajectory on the sky locates it at the center of the SNR, 6000-8000 yr ago, a unique characteristic among the sample. Spectra allow a stellar parameter determination and a chemical abundance analysis. In conclusion, we have a candidate to be the surviving companion of the SN Ia that resulted in SNR G272.2-3.2. It is supported by its kinematical characteristics and its trajectory within the SNR. This opens the possibility of a single-degenerate scenario for an SN Ia with an M-type dwarf companion.