High-resolution infrared laser spectroscopy is used to study acetylene-magnesium complexes formed in helium nanodroplets. The rotational fine structure observed in the spectrum of the binary complex is well described by a gas-phase Hamiltonian and is used to determine that the structure is T-shaped, with the magnesium binding weakly to the triple bond of the acetylene. The binary complex has a dipole moment of 0.39 +/- 5, as measured by Stark spectroscopy. Difference electron density maps reported herein reveal that this dipole moment arises from a strong polarization of the magnesium charge cloud by the quadrupole moment of the acetylene. Preliminary spectra are also reported for acetylene-Mg-n (n = 2, 3). Although these are not fully rotationally resolved, comparisons with ab initio calculations reported here provide some insights into the nature of these complexes.