Aging populations may be associated with increased nutritional risk, malnutrition, and food insecurity. This study aims to examine the relationship between food insecurity and nutritional risk, taking into account selected characteristics of the study group, and factors describing nutritional risk. It was conducted between May and July 2021, among 417 people aged 60 and older, in two regions of Poland. Questions from the SCREEN-14 questionnaire were used to assess nutritional risk. Selected questions from the HFSS questionnaire (U.S. Household Food Security Survey Module) concerning the elderly were used to assess food insecurity. A K-means cluster analysis was used to separate homogeneous clusters into food security indicators and nutritional risk factors. The Mann–Whitney U test and Kruskal–Wallis test were used to compare mean values between groups, and the Chi-square test was used to verify the differences. Two clusters were distinguished: I—“low food security and high nutritional risk” and II—“high food security and low nutritional risk”. Cluster I included people aged 60–65, and over 75, living in urban areas, living alone or with family, with unfavorable economic situations and family relationships. Cluster II was composed of people aged 71–75, who were rural residents, living with a partner, with favorable economic situations and family relations. The vast majority of nutritional risk factors were found in Cluster I and among those at high nutritional risk. The largest number of people were affected by such nutritional risk factors such as difficulty in chewing or biting, loss in appetite, skipping meals, and perceiving one’s weight as abnormal. Moreover, the group of people most significantly affected by high nutritional risk were in unfavorable economic situations, had poor family relationships, lived alone or with family, rated their health as worse than their peers, were overweight and obese, had metabolic disease, or impeding mobility. The results obtained can be applied to the planning of social and health policies for the elderly in Poland.