Once considered a phenotypically monomorphic bacterium, there is a growing body of work demonstrating heterogeneity among Mycobacterium tuberculosis (Mtb) strains in clinically relevant characteristics, including virulence and response to antibiotics. However, the genetic and molecular basis for most phenotypic differences among Mtb strains remains unknown. To investigate the basis of strain variation in Mtb, we performed genome-wide transposon mutagenesis coupled with next-generation sequencing (TnSeq) for a panel of Mtb clinical isolates and the reference strain H37Rv to compare genetic requirements for in vitro growth across these strains. We developed an analytic approach to identify quantitative differences in genetic requirements between these genetically diverse strains, which vary in genomic structure and gene content. Using this methodology, we found differences between strains in their requirements for genes involved in fundamental cellular processes, including redox homeostasis and central carbon metabolism. Among the genes with differential requirements were katG, which encodes the activator of the first-line antitubercular agent isoniazid, and glcB, which encodes malate synthase, the target of a novel small-molecule inhibitor. Differences among strains in their requirement for katG and glcB predicted differences in their response to these antimicrobial agents. Importantly, these strain-specific differences in antibiotic response could not be predicted by genetic variants identified through whole genome sequencing or by gene expression analysis. Our results provide novel insight into the basis of variation among Mtb strains and demonstrate that TnSeq is a scalable method to predict clinically important phenotypic differences among Mtb strains.