In genome evolution, genetic variants are the source of diversity, which natural selection acts upon. Treatment of human tuberculosis (TB) induces a strong selection pressure for the emergence of antibiotic resistance-conferring variants in the infecting Mycobacterium tuberculosis (MTB) strains. MTB evolution in response to treatment has been intensively studied and mainly attributed to point substitutions. However, the frequency and contribution of insertions and deletions (indels) to MTB genome evolution remains poorly understood. Here, we analyzed a multi-drug resistant MTB outbreak for the presence of high-quality indels and substitutions. We find that indels are significantly enriched in genes conferring antibiotic resistance. Furthermore, we show that indels are inherited during the outbreak and follow a molecular clock with an evolutionary rate of 5.37e-9 indels/site/year, which is 23 times lower than the substitution rate. Inherited indels may co-occur with substitutions in genes along related biological pathways; examples are iron storage and resistance to second-line antibiotics. This suggests that epistatic interactions between indels and substitutions affect antibiotic resistance and compensatory evolution in MTB.