Potato (Solanum tuberosum L.) is the fourth most important crop worldwide. Potato virus A (PVA) is one of the most harmful viruses infecting potatoes. However, the molecular mechanisms governing the responses to PVA infection in potato at the transcriptional and post-transcriptional levels are not well understood. In this study, we performed both mRNA and small RNA sequencing in potato leaves to identify the genes and miRNAs involved in the response to PVA infection. A total of 2,062 differentially expressed genes (DEGs) and 201 miRNAs (DEMs) were identified, respectively. Gene ontology (GO) and KEGG analysis revealed that these DEGs were involved in the transduction of pathogen signals, transcriptional reprogramming, induction of hormone signaling, activation of pathogenesis-related (PR) genes, and changes in secondary metabolism. Small RNA sequencing revealed 58 miRNA-mRNA interactions related to PVA infection. Some of the miRNAs (stu-miR482d-3p, stu-miR397-5p, etc) which target PR genes showed negative correlations between the DEMs and DEGs. Eight of the DEGs and three DEMs with their target genes were further validated by quantitative real time-PCR (qRT-PCR). Overall, this study provides a transcriptome-wide insight into the molecular basis of resistance to PVA infection in potato leaves and potenital candidate genes for improving resistance cultivars.