Considering the importance of magnesium-bearing hydrocarbon molecules (MgCnH; n = 2, 4, and 6) in the carbon-rich circumstellar envelopes (e.g., IRC+10216), a total of 28 constitutional isomers of MgC4H have been theoretically investigated using density functional theory (DFT) and coupled-cluster methods. The zero-point vibrational energy corrected relative energies at the ROCCSD(T)/cc-pCVTZ level of theory reveal that the linear isomer, 1-magnesapent-2,4-diyn-1-yl (1, 2Σ+), is the global minimum geometry on the MgC4H potential energy surface. The latter has been detected both in the laboratory and in the evolved carbon star, IRC+10216. The calculated spectroscopic data for 1 match well with the experimental observations (error ∼ 0.78%) which validates our theoretical methodology. Plausible isomerization processes happening among different isomers are examined using DFT and coupled-cluster methods. CASPT2 calculations have been performed for a few isomers exhibiting multireference characteristics. The second most stable isomer, 1-ethynyl-1λ3-magnesacycloprop-2-ene-2,3-diyl (2, 2A1, μ = 2.54 D), is 146 kJ mol-1 higher in energy than 1 and possibly the next promising candidate to be detected in the laboratory or in the interstellar medium in future.