As well as spreading through virions, influenza A viruses (IAVs) can evade antiviral drugs and neutralising antibodies by spreading directly from cell to cell. In cell culture this can occur by the induction of intercellular membrane connections known as tunnelling nanotube-like structures (TLSs), which are capable of trafficking the viral genome between cells. Here, we showed that TLSs are present at the site of IAV infections in vivo, and then used in vitro models to ask how IAVs induce their formation. We found that TLS induction cannot be induced by cytokine signalling from infected to uninfected cells, but requires IAV replication within cells. IAV replication can form filamentous virions with structural similarities to TLSs, but we found that TLS induction is independent of virion morphology. We therefore looked at the intracellular responses to infection. Using a pan-caspase inhibitor, we found that TLS induction by IAVs requires the onset of apoptosis. Our results, which suggest that IAVs control their ability to spread directly from cell to cell by driving infected cells into apoptosis, identifies a new way in which a virus can manipulate its host to evade antiviral immune responses.