Fanconi anemia (FA) is a rare genetic disorder characterized by genomic instability, developmental defects, and bone marrow (BM) failure. Hematopoietic stem cells (HSCs) in BM interact with the mesenchymal stem/stromal cells (MSCs); and this partly sustains the tissue homeostasis. MicroRNAs (miRNAs) can play a critical role during these interactions possibly via paracrine mechanisms. This is the first study addressing the miRNA profile of FA BM–MSCs obtained before and after BM transplantation (preBMT and postBMT, respectively). Non-coding RNA expression profiling and quality control analyses were performed in Donors (n = 13), FA preBMT (n = 11), and FA postBMT (n = 6) BM–MSCs using GeneChip miRNA 2.0 Array. Six Donor-FA preBMT pairs were used to identify a differentially expressed miRNA expression signature containing 50 miRNAs, which exhibited a strong correlation with the signature obtained from unpaired samples. Five miRNAs (hsa-miR-146a-5p, hsa-miR-148b-3p, hsa-miR-187-3p, hsa-miR-196b-5p, and hsa-miR-25-3p) significantly downregulated in both the paired and unpaired analyses were used to generate the BM–MSCs’ miRNA—BM mononuclear mRNA networks upon integration of a public dataset (GSE16334; studying Donor versus FA samples). Functionally enriched KEGG pathways included cellular senescence, miRNAs, and pathways in cancer. Here, we showed that hsa-miR-146a-5p and hsa-miR-874-3p were rescued upon BMT (n = 3 triplets). The decrease in miR-146a-5p was also validated using RT-qPCR and emerged as a strong candidate as a modulator of BM mRNAs in FA patients.