Aim The relationship between physical performance and cognition is well established. However, findings on the relationship between global cognition and the incidence of functional disability has been inconsistent. Using data from the International Mobility in Aging Study, we investigated the relationship between baseline cognitive function and the incidence of poor physical performance 2 years later. Methods A total of 1071 community‐dwelling participants (aged 64–75 years) from four sites in Canada and Latin America, with a Short Physical Performance Battery score ≥9 at baseline (good performance) were included. We carried out two sets of analyses, measuring cognition with either the Leganés Cognitive Test or the Montreal Cognitive Assessment. We used three logistic regression models, controlling for either no confounders, sociodemographic confounders or sociodemographic and health confounders. The full model was also stratified by site. A score <9 on the Short Physical Performance Battery indicated poor physical performance. Results In the fully adjusted model, each 1‐point increase in the baseline Leganés Cognitive Test score (range 0–32) was associated with a 10% decrease in the odds of incidence of poor physical performance at the 2‐year follow‐up ( P = 0.019). Likewise, each 1‐point increase in the baseline Montreal Cognitive Assessment score (range 0–30) was associated with a 16% decrease in the odds of developing poor physical performance ( P = 0.005). When stratified by site, the results were significant at the Latin American sites ( P = 0.02), but not at the Canadian sites ( P = 0.08). Conclusions Poor baseline cognition is associated with the incidence of poor physical performance in community‐dwelling older adults. To prevent physical disability, interventions addressing both cognitive and physical performance are required. Geriatr Gerontol Int 2020; ••: ••–•• .