In this work, we present a novel fault injection solution (ThorFI) for virtual networks in cloud computing infrastructures. ThorFI is designed to provide non-intrusive fault injection capabilities for a cloud tenant, and to isolate injections from interfering with other tenants on the infrastructure. We present the solution in the context of the OpenStack cloud management platform, and release this implementation as open-source software. Finally, we present two relevant case studies of ThorFI, respectively in an NFV IMS and of a high-availability cloud application. The case studies show that ThorFI can enhance functional tests with fault injection, as in 4%-34% of the test cases the IMS is unable to handle faults; and that despite redundancy in virtual networks, faults in one virtual network segment can propagate to other segments, and can affect the throughput and response time of the cloud application as a whole, by about 3 times in the worst case.