We establish a heralded interaction between two remotely trapped single (40)Ca(+) ions through the exchange of single photons. In the sender ion, we release single photons with a controlled temporal shape on the P(3/2) to D(5/2) transition and transmit them to the distant receiver ion. Individual absorption events in the receiver ion are detected by quantum jumps. For continuously generated photons, the absorption reduces significantly the lifetime of the long-lived D(5/2) state. For triggered single-photon transmission, we observe a coincidence between the emission at the sender and quantum jump events at the receiver.