Introduction: The aim of the study was to evaluate the neurocognitive safety of two schemes of general anesthesia based on propofol or sevoflurane applied to patients undergoing laparoscopic gynecological operations, with a special focus on the patients’ age, American Society of Anesthesiologists (ASA) physical status/risk category I, II, or III, and levels of neuromarkers. Material and methods: The Montreal Cognitive Assessment (MoCA) was chosen for cognitive assessment. The potential neuroinjury after anesthesia and operation was assessed with a set of neuromarkers: glial fibrillary acidic protein (GFAP), neurofilament light chain (NFL), tau protein (tau), and ubiquitin C-terminal hydrolase L1 (UCH-L1). The study was conducted on a group of women with no prior neurological or psychiatric diseases. Results: A total of 61 patients (mean age 40.57 years) were included in the study (29 patients under propofol-based anesthesia [PBA], 32 patients under sevoflurane-based anesthesia [SBA]). The groups were demographically comparable. The patients in both groups exhibited a postoperative increase in the MoCA regardless of the type of anesthesia. The NFL and UCH-L1 levels increased significantly in both groups. The GFAP levels were significantly higher in the SBA group. Neither the age nor the increase in the neuromarkers influenced the patients’ cognition. Conclusions: The types of anesthesia applied in the laparoscopic gynecological operations resulted in a cognitively safe outcome despite detectable alterations in the neuromarkers.