Background Breast cancer cases are on the rise in Ghana, with older adult women being more at risk of the disease. However, there is a paucity of current studies on factors that predict breast cancer screening among older adult women using nationally representative data. The present study, therefore, addressed this gap by estimating the prevalence of and identifying the factors that predict breast cancer screening among older adult women in Ghana. Methods We used the cross-sectional survey dataset of the 2014/2015 (wave II) Study on global AGEing and adult health (SAGE). A complex survey design methodology was employed to estimate the prevalence of breast cancer screening and the descriptive statistics of the demographic characteristics of the respondents. We used the firth logistic regression for the bivariate and multivariate analysis. Results The estimated breast cancer prevalence among older Ghanaian adult women was 4.5%. Older Ghanaian adult women who have screened for cervical cancer [AOR: 13.29; CI: 6.12, 28.84], had attained some primary education [AOR: 3.70; CI: 1.94, 7.07], junior secondary [AOR: 4.02; CI: 1.75, 9.21], senior secondary and higher [AOR: 4.57; CI: 2.15, 9.71], and have ever participated in a club meeting [AOR: 1.85; CI: 1.05, 3.24] were more likely to screen for breast cancer. Conclusion The significant predictors of breast cancer screening were cervical cancer screening status, formal education, and participation in club meetings. Given that the prevalence of breast cancer screening among the older adult women in Ghana is low, we recommend that policies and programs dedicated to encouraging women to screen for breast cancer should aim at giving women the opportunity to obtain higher formal education, encouraging women to be actively involved in club meetings and to intensify efforts to encourage women to screen for breast cancer.