Orf is a zoonotic disease that has caused huge economic losses globally. Systematical analysis of dysregulated cellular micro RNAs (miRNAs) in response to Orf virus (ORFV) infection has not been reported. In the current study, miRNA sequencing and RNA sequencing (RNA-seq) were performed in goat skin fibroblast (GSF) cells at 0, 18, and 30 h post infection (h.p.i). We identified 140 and 221 differentially expressed (DE) miRNAs at 18 and 30 h.p.i, respectively. We also identified 729 and 3961 DE genes (DEGs) at 18 and 30 h.p.i, respectively. GO enrichment analysis indicates enrichment of apoptotic regulation, defense response to virus, immune response, and inflammatory response at both time points. DE miRNAs and DEGs with reverse expression were used to construct miRNA-gene networks. Seven DE miRNAs and seven DEGs related to “negative regulation of viral genome replication” were identified. These were validated by RT-qPCR. Cfa-let-7a, a significantly upregulated miRNA, was found to repress Thrombospondin 1 (THBS1) mRNA and protein expression by directly targeting the THBS1 3′ untranslated region. THBS1 has been reported to induce apoptosis; therefore, the cfa-let-7a-THBS1 axis may play an important role in cellular apoptosis during ORFV infection. This study provides new insights into ORFV and host cell interaction mechanisms.