An innovative approach based on topology optimization is presented to define the optimal reinforcing layout for masonry arches and barrel vaults that have to be retrofitted using a prescribed amount of unidirectional fiber-reinforced composite strips. The overall elastic energy of the strengthened element is adopted as objective function to be minimized. The negligible tensile strength of brickwork is taken into account by using a no-tension elastic model. Conversely, the strength in the reinforcing fibers is constrained to be non-negative. To ensure perfect bonding of the strengthening layer at the intrados, suitable fasteners have to be employed. Preliminary numerical simulations are presented to assess the capabilities of the proposed procedure and to investigate the optimal reinforcement patterns for arches and barrel vaults. Fiber-reinforcement is found to spontaneously arise where cracks would occur in the unreinforced element. The proposed formulation allows also the optimal location of reinforcing steel ties to be spotted out.