In the present study, we developed near-infrared (NIR)-responsive shell-crosslinked (SCL) micelles using the Diels–Alder (DA) click reaction between an amphiphilic copolymer poly(d,l-lactide)₂₀-b-poly((furfuryl methacrylate)₁₀-co-(N-acryloylmorpholine)₇₈) (PLA₂₀-b-P(FMA₁₀-co-NAM₇₈)) and a diselenide-containing crosslinker, bis(maleimidoethyl) 3,3′-diselanediyldipropionoate (BMEDSeDP). The PLA₂₀-b-P(FMA₁₀-co-NAM₇₈) copolymer was synthesized by RAFT polymerization of FMA and NAM using a PLA₂₀-macro-chain transfer agent (PLA₂₀-CTA). The DA reaction between BMEDSeDP and the furfuryl moieties in the copolymeric micelles in water resulted in the formation of SCL micelles. The SCL micelles were analyzed by ¹H-NMR, FE-SEM, and DLS. An anticancer drug, doxorubicin (DOX), and an NIR sensitizer, indocyanine green (ICG), were effectively incorporated into the SCL micelles during the crosslinking reaction. The DOX/ICG-loaded SCL micelles showed pH- and NIR-responsive drug release, where burst release was observed under NIR laser irradiation. The in vitro cytotoxicity analysis demonstrated that the SCL was not cytotoxic against normal HFF-1 cells, while DOX/ICG-loaded SCL micelles exhibited significant antitumor activity toward HeLa cells. Thus, the SCL micelles of PLA₂₀-b-P(FMA₁₀-co-NAM₇₈) can be used as a potential delivery vehicle for the controlled drug release in cancer therapy.