The coronavirus 2019 (COVID-19) respiratory disease is caused by the novel coronavirus SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2), which uses the enzyme ACE2 to enter human cells. This disease is characterized by important damage at a multi-organ level, partially due to the abundant expression of ACE2 in practically all human tissues. However, not every organ in which ACE2 is abundant is affected by SARS-CoV-2, which suggests the existence of other multi-organ routes for transmitting the perturbations produced by the virus. We consider here diffusive processes through the protein-protein interaction (PPI) network of proteins targeted by SARS-CoV-2 as an alternative route. We found a subdiffusive regime that allows the propagation of virus perturbations through the PPI network at a significant rate. By following the main subdiffusive routes across the PPI network, we identify proteins mainly expressed in the heart, cerebral cortex, thymus, testis, lymph node, kidney, among others of the organs reported to be affected by COVID-19.