Although largely confined to the airways, SARS-CoV-2 infection has been associated with sensory abnormalities that manifest in both acute and chronic phenotypes. To gain insight on the molecular basis of these sensory abnormalities, we used the golden hamster model to characterize and compare the effects of infection with SARS-CoV-2 and influenza A virus (IAV) on the sensory nervous system. We detected SARS-CoV-2 transcripts but no infectious material in the cervical and thoracic spinal cord and dorsal root ganglia (DRGs) within the first 24 hours of intranasal virus infection. SARS-CoV-2-infected hamsters exhibited mechanical hypersensitivity that was milder but prolonged compared with that observed in IAV-infected hamsters. RNA sequencing analysis of thoracic DRGs 1 to 4 days after infection suggested perturbations in predominantly neuronal signaling in SARS-CoV-2-infected animals as opposed to type I interferon signaling in IAV-infected animals. Later, 31 days after infection, a neuropathic transcriptome emerged in thoracic DRGs from SARS-CoV-2-infected animals, which coincided with SARS-CoV-2-specific mechanical hypersensitivity. These data revealed potential targets for pain management, including the RNA binding protein ILF3, which was validated in murine pain models. This work elucidates transcriptomic signatures in the DRGs triggered by SARS-CoV-2 that may underlie both short- and long-term sensory abnormalities.