In the area of drug delivery aided by stimuli-responsive polymers, the biodegradability of nanocarriers is one of the major challenges that needs to be addressed with the utmost sincerity. Herein, a hydrogen sulfide (H2S) responsive hydrophobic dansyl-based trigger molecule is custom designed and successfully incorporated into the water-soluble polyurethane backbone, which is made of esterase enzyme susceptible urethane bonds. The amphiphilic polyurethanes, PUx (x = 2 and 3) with a biotin chain end, formed self-assembled nanoaggregates. A hemolysis and cytotoxicity profile of doxorubicin (DOX)-loaded biotinylated PU3 nanocarriers revealed that it is nonhemolytic and has excellent selectivity toward HeLa cells (biotin receptor-positive cell lines) causing ∼60% cell death while maintaining almost 100% cell viability for HEK 293T cells (biotin receptor-negative cell lines). Furthermore, better cellular internalization of DOX-loaded fluorescent nanocarriers in HeLa cells than in HEK 293T cells confirmed receptor-mediated endocytosis. Thus, this work ensures that the synthesized polymers serve as biodegradable nanocarriers for anticancer therapeutics.