In this Rapid Communication, we have examined the superconducting ground state of the HfV2Ga4 compound using resistivity, magnetization, zero-field (ZF), and transverse-field (TF) muon-spin relaxation and rotation (μSR) measurements. Resistivity and magnetization unveil the onset of bulk superconductivity with TC∼3.9 K. TF-μSR measurements show the temperature dependence of the superfluid density, indicating, surprisingly, a nodal two-gap s+d-wave superconducting order parameter. In addition, the ZF muon relaxation rate increases with decreasing temperature below 4.6 K, suggesting the presence of weak spin fluctuations. These observations pointed to an unconventional multiband nature of the superconducting ground state. To better understand these findings, we carry out first-principles electronic-structure calculations, further highlighting multiple disconnected sheets with very different orbital weights and spin-orbit coupling composing the Fermi surface, bridging the way for a nodal multiband superconductivity scenario. In this vein, therefore, the HfV2Ga4 family stands out as an open avenue to novel unexplored unconventional superconducting compounds and an ideal playground to investigate the mechanisms behind such phenomena.