Long-lived adult stem cells could accumulate non-repaired DNA damage or mutations that increase the risk of tumor formation. To date, studies on mutations in stem cells have concentrated on clonal (homoplasmic) mutations and have not focused on rarely occurring stochastic mutations that may accumulate during stem cell dormancy. A major challenge in investigating these rare mutations is that conventional next generation sequencing (NGS) methods have high error rates. We have established a new method termed Duplex Sequencing (DS), which detects mutations with unprecedented accuracy. We present a comprehensive analysis of mitochondrial DNA mutations in human breast normal stem cells and non-stem cells using DS. The vast majority of mutations occur at low frequency and are not detectable by NGS. The most prevalent point mutation types are the C>T/G>A and A>G/T>C transitions. The mutations exhibit a strand bias with higher prevalence of G>A, T>C, and A>C mutations on the light strand of the mitochondrial genome. The overall rare mutation frequency is significantly lower in stem cells than in the corresponding non-stem cells. We have identified common and unique non-homoplasmic mutations between non-stem and stem cells that include new mutations which have not been reported previously. Four mutations found within the MT-ND5 gene (m.12684G>A, m.12705C>T, m.13095T>C, m.13105A>G) are present in all groups of stem and non-stem cells. Two mutations (m.8567T>C, m.10547C>G) are found only in non-stem cells. This first genome-wide analysis of mitochondrial DNA mutations may aid in characterizing human breast normal epithelial cells and serve as a reference for cancer stem cell mutation profiles.