RNAi is an evolutionary conserved, highly efficient, and cost effective technique of gene silencing. It holds considerable promise and success has been achieved both in vitro and in vivo experiments. However, it is not devoid of undesirable side effects as dsRNA can trigger the immune response and can also cause non-specific off-target gene silencing. In the present study, silencing of myostatin gene, a negative regulator of myogenesis, was evaluated in caprine fetal fibroblasts using three different shRNA constructs. Out of these three constructs, two constructs sh1 and sh2 showed, 72% and 50% reduction (p < 0.05) of myostatin mRNA, respectively. Efficient suppression (42–86%) of MSTN gene (p < 0.05) was achieved even by reducing the concentration of shRNA constructs. The induction of classical interferon stimulated gene (Oligoandenylate Synthetase-1, OAS-1) was studied to analyze the immune response against shRNAs. Notably, a reduction in the potency of shRNAs to induce interferon response was observed at lower concentration for OAS1 gene. The results obtained in the study would be helpful in the abrogation of the bystander effects of RNAi for long term stable expression of anti-MSTN expression constructs in the muscle.