Fibrosis is a pathological process characterized by the excessive deposition of extracellular matrix in the tissue's extracellular space, leading to structural injury and organ dysfunction, and even organ failure, posing a threat to human life. Despite mounting evidence suggesting that fibrosis is reversible, effective treatments for fibrotic diseases are lacking. Accumulating evidence has elucidated that ribonucleic acid (RNA) modifications have emerged as novel mechanisms regulating gene expression. N6-methyladenosine (m6A) modification is a well-known prevalent RNA posttranscriptional modification that participates in essential biological processes such as RNA splicing, translation, and degradation. It is tightly implicated in a wide range of cellular processes and various human diseases, particularly in organ fibrosis. The m6A modification is a dynamic and reversible process regulated by methylases, commonly known as "writers," and demethylases referred to as "erasers," while m6A modifications are recognized by "readers." Accumulating evidence suggests that m6A modification on RNAs is tightly associated with fibrotic diseases of visceral organs including the lungs, heart, liver, and kidney. In this review, recent advances in the impact of m6A methylation of RNAs on visceral organ fibrosis are highlighted and the potential prospects for therapy in treating fibrotic diseases of visceral organs are discussed.