DNA nanostructures are emerging as a versatile platform for controlled drug delivery as a result of recent progress in production yield and strategies to obtain prolonged stability in biological environments. The construction of nanostructures from this unique biomaterial provides unparalleled control over structural and functional parameters. Recent applications of DNA origami-based nanocarriers for therapeutic drug delivery in preclinical phases highlight them as promising alternatives to conventional nanomaterials, as they benefit from the inherent favorable properties of DNA including biocompatibility and precise spatial addressability. By incorporating targeting aptamers and responsive properties into the nanocarrier design, more selective DNA origami-based nanocarriers are successfully prepared. On the other hand, current systems remain poorly understood in terms of biodistribution, final fate, and controlled drug release. As such, advances are needed to translate this material platform in its full potential for therapeutic applications.