The search for extra dimensions is a challenging endeavor to probe physics beyond the Standard Model. The joint detection of gravitational waves (GW) and electromagnetic (EM) signals from the merging of a binary system of compact objects like neutron stars can help constrain the geometry of extra dimensions beyond our 3 + 1 spacetime ones. A theoretically well-motivated possibility is that our observable Universe is a 3 + 1-dimensional hypersurface, or brane, embedded in a higher 4 + 1-dimensional antide Sitter (AdS(5)) spacetime, in which gravity is the only force which propagates through the infinite bulk space, while other forces are confined to the brane. In these types of brane-world models, GW and EM signals between two points on the brane would, in general, travel different paths. This would result in a time lag between the detection of GW and EM signals emitted simultaneously from the same source. We consider the recent near-simultaneous detection of the GW event GW170817 from the LIGO/Virgo collaboration, and its EM counterpart, the short gamma-ray burst GRB170817A detected by the Fermi Gamma-ray Burst Monitor and the International Gamma-Ray Astrophysics Laboratory Anti-Coincidence Shield spectrometer. Assuming the standard.-cold dark matter scenario and performing a likelihood analysis which takes into account astrophysical uncertainties associated to the measured time lag, we set an upper limit of l less than or similar to 0.535 Mpc at 68% confidence level on the AdS(5) radius of curvature l. Although the bound is not competitive with current Solar System constraints, it is the first time that data from a multimessenger GW-EM measurement is used to constrain extra-dimensional models. Thus, our work provides a proof of principle for the possibility of using multimessenger astronomy for probing the geometry of our space-time.