Micronutrient malnutrition is a global health problem. An improved understanding of the genetic variation of important micronutrient traits within a potato breeding population will help devise breeding strategies for the biofortification of this important food staple. The dataset consisted of 556 individuals from 17 full-sib diploid families grown in 2006 in Huanuco, Peru, and 1329 individuals from 32 full-sib families grown in 2009 in Ayacucho, Peru. Genetic parameters were estimated using univariate and multivariate individual Bayesian models for micronutrient tuber content including Fe and Zn. Genetic variance was additive and heritability estimates were moderate (0.36 to 0.57) and inflated if the common environment of full-sibs was not taken into account. Posterior modes of genetic correlation estimates between minerals, when analyzed on a dry-weight basis, were all positive (0.04 to 0.72) and between minerals and tuber dry matter were negative (-0.14 to-0.38). On a fresh-weight basis, genetic correlations between minerals and tuber dry matter were small but positive (0.05 to 0.18). The implications and challenges for selective breeding to enhance micronutrient content in potato tubers are discussed.