Lipoprotein(a) [Lp(a)] is an established atherosclerotic cardiovascular risk factor, but its association with stroke is less consistent than that with coronary disease and appears to depend on stroke subtype and the degree of Lp(a) elevation. We examined whether baseline Lp(a) was associated with incident total stroke in 1113 Taiwanese women who met an amenorrhea-based definition of postmenopausal status in the Chin-Shan Community Cardiovascular Cohort. Because contemporary data suggest that Lp(a)-related stroke risk is most evident for ischemic stroke and at very high concentrations, cohort-specific 75th (20.05 mg/dL) and 90th (36.55 mg/dL) percentiles were treated as internal exposure rankings rather than clinical cutoffs. During a mean follow-up of 8.6 years, 55 total strokes and 25 coronary artery disease (CAD) events occurred. After adjustment for age, body mass index, hypertension, diabetes mellitus, smoking, LDL cholesterol, and triglycerides, Lp(a) ≥ 75th percentile was associated with total stroke (HR 1.81, 95% CI 1.02–3.21; p = 0.04), with a higher point estimate at ≥90th percentile (HR 2.45, 95% CI 1.26–4.76; p = 0.01). CAD estimates were imprecise and not statistically significant. These findings provide hypothesis-generating risk-marker evidence from an underrepresented East Asian population but do not establish ischemic-stroke specificity, a menopause-specific mechanism, a lower clinical Lp(a) threshold, or a stronger association with stroke than CAD.