Engagement of innate viral sensors elicits a robust antiviral program via the induction of type I interferons (IFNs). Innate defense mechanisms against ssDNA viruses are not well defined. Here, we examine type I IFN induction and effectiveness in controlling a ssDNA virus. Using mouse embryonic fibroblasts (MEFs), we found that a murine parvovirus, minute virus of mice (MVMp), induced a delayed but significant IFN response. MEFs deficient in mitochondrial antiviral signaling protein (MAVS) mounted a wild-type IFN response to MVMp infection, indicating that RIG-I-dependent RNA intermediate recognition is not required for innate sensing of this virus. However, MVMp-induced IFNs, as well recombinant type I IFNs, were unable to inhibit viral replication. Finally, MVMp infected cells became unresponsive to Poly (I:C) stimulation. Together, these data suggest that the MVMp efficiently evades antiviral immune mechanisms imposed by type I IFNs, which may in part explain their efficient transmission between mice.