Carbon molecules and their ^13^C-isotopologues can be used to determine the ^12^C/^13^C abundance ratios in stellar and interstellar objects. C3 is a pure carbon chain molecule found in star forming regions and in stellar shells of carbon-rich late-type stars. Latest laboratory data of ^13^C-isotopologues of C3 allow a selective search for the mono-substituted species ^13^CCC and C^13^CC based on accurate ro-vibrational frequencies. Our aim was to provide the first detection of the ^13^C-isotopologues ^13CCC and C^13^CC in space and to derive the ^12^C/ ^13^C ratio of interstellar gas in the massive star-forming region SgrB2(M) near the Galactic Center. We used the heterodyne receivers GREAT and upGREAT on board SOFIA to search for the ro-vibrational transitions Q(2) and Q(4) of ^13^CCC and C^13^CC at 1.9THz along the line of sight towards SgrB2(M). In addition, to determine the local excitation temperature we analyzed data from nine ro-vibrational transitions of the main isotopologue CCC in the frequency range between 1.6-1.9THz which were taken from the Herschel Science Data Archive. We report the first detection of the isotopologues ^13^CCC and C^13^CC. For both species the ro-vibrational absorption lines Q(2) and Q(4) have been identified, primarily arising from the warm gas physically associated with the strong continuum source SgrB2(M). From the available CCC ro-vibrational transitions we derived a gas excitation temperature of Tex=44.4^+4.7^_-3.9_K and a total column density of N(CCC)=3.88^+0.39^_-0.35_x10^15^cm^-2.. Assuming the excitation temperatures of C^13^CC and ^13^CCC to be the same as for CCC, we obtained column densities of the ^13^C-isotopologues of N(C^13^CC)=2.1^+0.9^_-0.6^_x10^14^cm^-2^ and N(^13^CCC)=2.4^+1.2^_-0.8_x10^14^cm^-2^. The derived ^12^C/^13^C abundance ratio in the C3 molecules is 20.5+/-4.2, which is in agreement with the elemental ratio of 20, typically observed in SgrB2(M). However, we find the N(^13^CCC)/N(C^13^CC) ratio to be 1.2+/-0.1, which is shifted from the statistically expected value of 2. We propose that the discrepant abundance ratio arises due to the the lower zero-point energy of C^13^CC which makes position- exchange reaction converting C^13^CC to C^13^CC energetically favorable.