The 4f-electron system YbAl3C3 with a nonmagnetic spin-dimer ground state has been studied by neutron diffraction in an applied magnetic field. A long-range magnetic order involving both ferromagnetic and antiferromagnetic components has been revealed above the critical field HC∼6 T at temperature T=0.05 K. The magnetic structure indicates that the geometrical frustration of the prototype hexagonal lattice is not fully relieved in the low-temperature orthorhombic phase. The suppression of magnetic ordering by the remanent frustration is the key factor stabilizing the nonmagnetic singlet ground state in zero field. Temperature-dependent measurements in the applied field H=12 T revealed that the long-range ordering persists up to temperatures significantly higher than the spin gap, indicating that this phase is not directly related to the singlet-triplet excitation. Combining our neutron diffraction results with the previously published phase diagram, we support the existence of an intermediate disordered phase as the first excitation from the nonmagnetic singlet ground state. Based on our results, we propose YbAl3C3 as a material for studying the quantum phase transitions of heavy-fermion metals under the influence of geometrical frustration.