An economically viable method to extract polyhydroxyalkanoates (PHAs) from cells is desirable for this biodegradable polymer of potential biomedical applications. In this work, two non-chlorinated solvents, cyclohexanone and γ-butyrolactone, were examined for extracting PHA produced by the bacterial strain Cupriavidus necator H16 cultivated on vegetable oil as a sole carbon source. The PHA produced was determined as a poly(3-hydroxybutyrate) (PHB) homopolyester. The extraction kinetics of the two solvents was determined using gel permeation chromatography (GPC). When cyclohexanone was used as the extraction solvent at 120 °C in 3 min, 95% of the PHB was recovered from the cells with a similar purity to that extracted using chloroform. With a decrease in temperature, the recovery yield decreased. At the same temperatures, the recovery yield of γ-butyrolactone was significantly lower. The effect of the two solvents on the quality of the extracted PHB was also examined using GPC and elemental analysis. The molar mass and dispersity of the obtained polymer were similar to that extracted using chloroform, while the nitrogen content of the PHB extracted using the two new solvents was slightly higher. In a nutshell, cyclohexanone in particular was identified as an expedient candidate to efficiently drive novel, sustainable PHA extraction processes.