(1) Background: Awareness and compliance with standard precautions (SPs) are essential health issues for both healthcare staff and patients. Hence, more research is urgently needed in the health sector worldwide, particularly in Arab countries. The purpose of this study was to investigate compliance with SPs among nurses and doctors, as well as challenges affecting their adherence to these SPs. (2) Methods: A cross-sectional descriptive study was conducted. The researchers administered the compliance with the Standard Precautions Scale (CAPS) to staff nurses and doctors from critical care units at a university-affiliated hospital in Jeddah, Kingdom of Saudi Arabia (KSA). A total of 112 nurses and 59 doctors were enrolled in the study to determine their compliance with SPs as well as the challenges affecting their adherence to these SPs. (3) Results: The overall mean percentage scores of nurses’ and doctors’ compliance with SPs were 36.43 ± 15.85% and 33.27 ± 15.76%, respectively. In addition, the current study identified associated challenges affecting these healthcare workers’ adherence to these SPs, including the effect of sociodemographic factors, such as age and experience. (4) Conclusions: The study found that both nurses and doctors had poor compliance with all SPs except for disposal of sharps, which scored with suboptimal compliance. Nurses’ compliance with recommended precautions varied significantly according to age, clinical experience, and attendance at training courses. Healthcare organizations should consider a holistic approach to promote adherence to SPs to enhance outcomes associated with optimized care delivery and stakeholder safety.