The use of biopolymer‐based drug delivery systems is increasing in the pharmaceutical area due to them biodegradable and biocompatible properties. In this work, a poly (butylene succinate) (PBS) grafted with poly (hydroxypropyl methacrylate) (PHPMA), PBSgPHPMA, is prepared using maleic unsaturations inserted in the PBS chain during its synthesis. Several characterization techniques are used to study the homopolymers and the grafted material. Among them, Fourier Transform Infrared (FTIR), Thermogravimetric analysis (TGA) Differential scanning calorimetry (DSC), and X‐ray diffraction (XRD) allowed inferring the obtaining of the aimed materials. Also, the copolymer is used to prepare microparticles containing Meloxicam by emulsification and solvent evaporation method. These microparticles are tested as drug delivery systems under pH 8.5 (gastrointestinal) and pH 5.5 (skin). The primary results allowed inferring that the grafted material can be used as a drug delivery system, showing that the release rate at pH 5.5 allowed the slower delivery rate among tested materials.