Biotransformation is a biotechnological process that allows obtaining other substances from a precursor using biocatalysts, which can be microorganisms. In this work, the yeast Pichia pastoris was used to catalyze reactions with three substrates, the monoterpenes α-pinene, β-pinene, and γ-terpinene. The most promising substrate was selected for studies for a shorter reaction period and using immobilized cells in calcium alginate. Initially, the reactions were carried out for 48 h using free cells in an aqueous medium containing glucose and substrate. After extraction with dichloromethane, substrates and products were analyzed by gas chromatography coupled to a mass spectrometer. Under these conditions, the three substrates underwent near total conversion. Biotransformation with α-pinene as substrate proved to be more promising because only one product was formed, 2-phenylethanol, which has a rose aroma and is of great industrial interest. The monoterpene α-pinene was tested in reactions for 24 h, but the conversion to 2-phenylethanol was around 50%. Then, the cells were immobilized in calcium alginate and used in 24-hour reactions. However, other products were formed, different from 2-phenylethanol. Therefore, it is concluded that obtaining 2-phenylethanol through the biotransformation of the monoterpene α-pinene by free cells of P. pastoris can be a promising bioprocess.