Background: The link between arterial stiffness and mild cognitive impairment (MCI) is receiving increasing attention, and the goal of this study was to explore the relationship among the ankle brachial index (ABI), brachial-ankle pulse wave velocity (Ba-PWV), and MCI in patients with acute lacunar infarction (ALI). Methods: A total of 103 hospitalized patients with ALI were divided into a non-MCI group (n = 41) and an MCI group (n = 62) according to their Montreal Cognitive Assessment (MoCA) scores. A binary logistic regression model was used to assess the association among ABI, Ba-PWV, and MCI after adjusting for confounding factors. Spearman correlation was utilized to analyse the correlations between ABI, Ba-PWV, and MoCA total scores and sub-scores in ALI patients. Results: Participants with cognitive impairment had significantly higher Ba-PWV and lower ABI than those with normal cognition. Correlation analysis suggested that Ba-PWV (r = −0.854, p < 0.05) and ABI (r = 0.734, p < 0.05) were correlated with MoCA total scores; of all MoCA sub-scores, visuospatial/executive function was the most strongly correlated with the vascular variables. In the binary logistic regression analysis, Ba-PWV (odds ratio [OR] = 4.507, 95% confidence interval [CI] = 2.152–9.441) and ABI (OR = 1.124, 95% CI = 1.015–1.254) were significantly associated with MCI, even after adjusting for lipoprotein (a) and systolic and diastolic blood pressure. Conclusion: The present study suggested that a higher Ba-PWV and a lower ABI were independent risk factors for MCI in patients with ALI.