Multiple imputation is a common technique for dealing with missing values and is mostly applied in regression settings. Its application in cluster analysis problems, where the main objective is to classify individuals into homogenous groups, involves several difficulties which are not well characterized in the current literature. In this paper, we propose a framework for applying multiple imputation to cluster analysis when the original data contain missing values. The proposed framework incorporates the selection of the final number of clusters and a variable reduction procedure, which may be needed in data sets where the ratio of the number of persons to the number of variables is small. We suggest some ways to report how the uncertainty due to multiple imputation of missing data affects the cluster analysis outcomes—namely the final number of clusters, the results of a variable selection procedure (if applied), and the assignment of individuals to clusters. The proposed framework is illustrated with data from the Phenotype and Course of Chronic Obstructive Pulmonary Disease (PAC-COPD) Study (Spain, 2004–2008), which aimed to classify patients with chronic obstructive pulmonary disease into different disease subtypes.