Excitons in two-dimensional semiconductors provide a novel platform for fundamental studies of many-body interactions. In particular, dipolar interactions between spatially indirect excitons may give rise to strongly correlated phases of matter that so far have been out of reach of experiments. Here we show that excitonic few-body systems in atomically thin transition-metal dichalcogenides confined to a one-dimensional geometry undergo a crossover from a Tonks-Girardeau to a charge density wave regime. To this end, we take into account realistic system parameters and predict the effective exciton-exciton interaction potential. We find that the pair-correlation function contains key signatures of the many-body crossover already at small exciton numbers and show that photoluminescence spectra provide readily accessible experimental fingerprints of these strongly correlated quantum many-body states.