Suicide prevention efforts often depend on the willingness or ability of people to disclose current suicidal behavior. The aim of this study is to identify characteristics that are associated with non-disclosure of suicidal ideation. Data from the Dutch cross-sectional survey Health Monitor 2016 were used, resulting in 14,322 respondents (age 19+). Multiple logistic regression analyses were conducted to assess the strength of the associations between demographics and health-related characteristics as independent variables, and non-disclosure of suicidal ideation as the dependent variable. The mean age of the respondents was 60 years (SD 16.7) and 45% were male. Of these adults, 5% (n = 719) reported suicidal ideation in the past year, nearly half of which (48%) did not disclose suicidal ideation. Non-disclosure was significantly associated with social loneliness (OR = 1.29). Inverse significant associations were found for age (35–49 years, OR = 0.53), poor health status (OR = 0.63), frequent suicidal ideation (OR = 0.48), and severe psychological distress (OR = 0.63). The accuracy of this model was fair (AUC = 0.73). To conclude, non-disclosure is a substantial problem in adults experiencing suicidal ideation. Adults who do not disclose suicidal ideation are more likely to have few social contacts, while they are less likely to experience poor (mental) health and frequent suicidal thoughts.