Background Ischemic stroke (IS) is a fatal complication of acute coronary syndrome (ACS). Factors that speed up IS development after ACS are understudied, especially in developing countries like Pakistan. Thus, this study was designed to identify the potential risk factors of IS in patients with a preceding episode of ACS. Methodology This retrospective study was performed on 208 patients whose ACS and its consequent complications such as IS were managed in the cardiac and neurology units of Benazir Bhutto Hospital, Rawalpindi, from January 2022 to March 2023. Patients were enrolled via consecutive sampling and pre-defined inclusion and exclusion criteria. Before data collection, informed consent and ethical approval were obtained. Data were retrieved from the medical records of the patients. A self-structured proforma was applied to collect data. SPSS version 25 (IBM Corp., Armonk, NY, USA) was used for data analysis. The study variables between patients with and without IS were compared using descriptive and inferential statistics. The association between IS and its possible risk factors in patients who had previously experienced ACS was determined using multivariate logistic regression. Results Of the 208 enrolled patients, 24 (11.54%) had IS following ACS. Sedentary lifestyle (odds ratio (OR) = 3.099, 95% confidence interval (CI) = 1.025~4.219, p = 0.009), hypertension (OR = 3.060, 95% CI = 1.798~4.876, p = 0.002), diabetes mellitus (OR = 2.899, 95% CI = 1.126~4.112, p = 0.009), dyslipidemia (OR = 2.907, 95% CI = 1.332~4.254, p = 0.007), history of smoking (OR = 2.760, 95% CI = 1.234~4.122, p = 0.018), and non-adherence to ACS medication (OR = 2.966, 95% CI = 1.300~4.266, p = 0.030), were the risk factors of IS among patients with preceding ACS. Conclusions In the study population, the incidence of IS following ACS was significant. Sedentary lifestyle, hypertension, diabetes mellitus, dyslipidemia, smoking history, and non-compliance with ACS therapy all played a significant role in the development of IS in patients with prior ACS. Proper management of ACS and associated risk factors could lead to the prevention of serious complications such as IS.