Handling missing values (MVs) and feature selection (FS) are vital preprocessing tasks for many pattern recognition, data mining, and machine learning (ML) applications, involving classification and regression problems. The existence of MVs in data badly affects making decisions. Hence, MVs have to be taken into consideration during preprocessing tasks as a critical problem. To this end, the authors proposed a new algorithm for manipulating MVs using FS. Bayesian ridge regression (BRR) is the most beneficial type of Bayesian regression. BRR estimates a probabilistic model of the regression problem. The proposed algorithm is dubbed as cumulative Bayesian ridge with similarity and Luca’s fuzzy entropy measure (CBRSL). CBRSL reveals how the fuzzy entropy FS used for selecting the candidate feature holding MVs aids in the prediction of the MVs within the selected feature using the Bayesian Ridge technique. CBRSL can be utilized to manipulate MVs within other features in a cumulative order; the filled features are incorporated within the BRR equation in order to predict the MVs for the next selected incomplete feature. An experimental analysis was conducted on four datasets holding MVs generated from three missingness mechanisms to compare CBRSL with state-of-the-art practical imputation methods. The performance was measured in terms of R2 score (determination coefficient), RMSE (root mean square error), and MAE (mean absolute error). Experimental results indicate that the accuracy and execution times differ depending on the amount of MVs, the dataset’s size, and the mechanism type of missingness. In addition, the results show that CBRSL can manipulate MVs generated from any missingness mechanism with a competitive accuracy against the compared methods.