(1) Background: The suicide of older adults shows different factors between the youngest-old adults and the old-old adults. This study aimed to identify factors predicting suicidal ideation among youngest-old adults (ages 65 to 74 years) and predict high-risk groups’ characteristics. (2) Methods: The subjects of this study were 970 youngest-old adults who participated in the Korean National Health and Nutrition Examination Survey (KNHANES VIII Year 1, 2019). Logistic regression analysis identified factors related to suicidal ideation, and decision tree analysis identified combined characteristics among high-risk groups. Data were analyzed using SPSS 27.0. (3) Results: Suicidal ideation became more common among those with relatively lower income levels (OR = 1.48, 95% CI = 1.04–2.12), those whom had experienced depression (OR = 9.28, 95% CI = 4.57–18.84), those with relatively higher stress levels (OR = 2.42, 95% CI = 1.11–5.28), and those reporting a relatively worse perceived health (OR = 1.88, 95% CI = 1.23–3.11). Complex characteristics that combined depression, low personal income level, and low perceived health predicted a high risk of suicidal ideation (64.6%, p < 0.05). (4) Conclusions: The findings indicate that this high-risk group should be prioritized when developing suicide prevention strategies.