The presence of hydroxyl groups in cyclodextrin (CD) makes it highly hydrophilic and simultaneously allows its chemical modification to graft polyurethane to control the drug release for longer period of time by maintaining the hydrophobic–hydrophilic balance through varying extent of grafting. Grafting of polyurethane on CD is confirmed through 1H NMR and molecular weight measurement while FTIR and UV visible studies further support grafting and emphasize the interaction among polymer chains as a whole. Degree of grafting is evaluated from the integrated peak area in NMR spectra. Thermal and mechanical measurements show improved stability and strength of the graft polymers with respect to pure CD. The conversion of particle nature of CD to strip‐like morphology in graft copolymers is evident from atomic force microscopy. Sustained drug release has been achieved using graft copolymer against burst release from pure CD and specific interactions, as observed through spectroscopy and thermal measurements, are responsible for sustained release of drug. Biocompatibility of graft copolymers has been checked using cellular studies through MTT assay and cell adhesion. Importantly, the cell killing efficiency has been demonstrated by embedding anticancer drug in polymer matrices causing mortality rate of 75% using graft copolymer against scanty 25% using pure drug or drug embedded in CD and the result is understood from the sustained release of drug from the graft copolymer vis‐à‐vis burst release in other systems. © 2018 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 107A: 434–444, 2019.