MicroRNAs play an important role in tumorigenesis and, among them, miR-21 is found to be aberrantly up-regulated in various tumors. The tumor-associated antigen, folate receptor alpha is a GPI-membrane protein overexpressed in many malignant tumors of epithelial origin, including ovarian and cervical cancers. Covalently bound octahedral DNA nanocages were functionalized with folate molecules and utilized as scaffolds to engineer four sequestering units with a miR-21 complementary sequence for obtaining biocompatible Fol-miR21-NC non-toxic nanostructures, to be able to selectively recognize folate receptor alpha-overexpressing cancer cells and sequester the oncogenic miR-21. qPCR assays showed that Fol-miR21-NCs reduce the miR-21 expression up to 80% in cancer cells in the first 2 days of treatment. Functional assays demonstrated that miR-21 sequestering leads to up-regulation of miR-21 tumor suppressor targets (i.e., PTEN and Pdcd4), reduction in cancer cell migration, reduction in proliferation, and increase in cell death. Fol-miR21-NCs can be efficiently loaded with the chemotherapeutic agent doxorubicin. Co-delivery of anti-miR-21 and doxorubicin showed additive cytotoxic effects on tumor cells, paving the way for their use as selective nucleic acid drugs.