High-angular-resolution cosmic microwave background experiments provide a unique opportunity to conduct a survey of time-variable sources at millimeter wavelengths, a population which has primarily been understood through follow-up measurements of detections in other bands. Here we report the first results of an astronomical transient survey with the South Pole Telescope (SPT) using the SPT-3G camera to observe 1500 square degrees of the southern sky. The observations took place from March to November 2020 in three bands centered at 95 GHz, 150 GHz, and 220 GHz. We detect 13 stellar flares from 8 stars, with in-band flare luminosities ranging between 1027 erg s-1 and 1030 ergs-1. There is evidence of coincident optical activity in the ASAS-SN variable stars database for two of the flares; one of the two also has simultaneous TESS coverage, allowing minute-scale comparison of the flare evolution at millimeter and optical wavelengths. The flare stars include M dwarfs, Rotational Variables, By Dra Variables, and RS CVn variables; all are X-ray sources except for the M dwarfs. Future data from SPT-3G and forthcoming instruments will provide real-time detection of millimeter stellar flares on a monthly basis.