Herein, we report a dynamic DNA nanostructure exhibiting switchable and size-selective molecular recognition properties. A DNA block copolymer, polystyrene-b-DNA (PS-b-DNA), and a thermo-responsive block copolymer, PS-b-poly(N-isopropylacrylamide) (PS-b-PNIPAM), were simultaneously assembled to form hybrid micelles composed of a PS core and a DNA/PNIPAM corona. PNIPAM strands did not significantly hinder the binding of molecular DNA for a broad range of PNIPAM lengths. On the other hand, they exerted significant steric hindrance for interactions with nanoscale species, which can be reversibly turned off by increasing the temperature above the lower critical solution temperature (LCST) of PNIPAM. Owing to the switchable and size-selective steric hindrance, the hybrid DNA micelles showed thermally controllable enzymatic degradation and cellular uptake. These results demonstrate that the binary self-assembly of two different responsive block copolymers is a promising approach to prepare dynamic nanostructures with controllable biological recognition properties.