Hepatitis C virus (HCV) is a positive single-stranded RNA virus of enormous global health importance, with direct-acting antiviral therapies replacing an immunostimulatory interferon-based regimen. The dynamics of HCV positive and negative-strand viral RNAs (vRNAs) under antiviral perturbations have not been studied at the single-cell level, leaving a gap in our understanding of antiviral kinetics and host-virus interactions. Here, we demonstrate quantitative imaging of HCV genomes in multiple infection models, and multiplexing of positive and negative strand vRNAs and host antiviral RNAs. We capture the varying kinetics with which antiviral drugs with different mechanisms of action clear HCV infection, finding the NS5A inhibitor daclatasvir to induce a rapid decline in negative-strand viral RNAs. We also find that the induction of host antiviral genes upon interferon treatment is positively correlated with viral load in single cells. This study adds smFISH to the toolbox available for analyzing the treatment of RNA virus infections.