In minibeam therapy, the sparing of deep-seated normal tissue is limited by transverse beam spread caused by small-angle scattering. Contrary to proton minibeams, helium or carbon minibeams experience less deflection, which potentially reduces side effects. To verify this potential, an irradiation facility for preclinical and clinical studies is needed. This manuscript presents a concept for a carbon minibeam irradiation facility based on a LINAC design for conventional carbon therapy. A quadrupole triplet focuses the LINAC beam to submillimeter minibeams. A scanning and a dosimetry unit are provided to move the minibeam over the target and monitor the applied dose. The beamline was optimized by TRAVEL simulations. The interaction between beam and these components and the resulting beam parameters at the focal plane is evaluated by TOPAS simulations. A transverse beamwidth of < 100 µm (σ) and a peak-to-valley (energy) dose ratio of > 1000 results for carbon energies of 100 MeV/u and 430 MeV/u (about 3 cm and 30 cm range in water) whereby the average beam current is about 30 nA. Therefore, the presented irradiation facility exceeds the requirements for hadron minibeam therapy.