Many-body interactions in monolayer transition-metal dichalcogenides are strongly affected by their unique band structure. We study these interactions by measuring the energy shift of neutral excitons (bound electron-hole pairs) in gated WSe2 and MoSe2. Surprisingly, while the blueshift of the neutral exciton X0 in electron-doped samples can be more than 10 meV, the blueshift in hole-doped samples is nearly absent. Taking into account dynamical screening and local-field effects, we present a transparent and analytical model that elucidates the crucial role played by intervalley plasmons in electron-doped conditions. The energy shift of X0 as a function of charge density is computed showing agreement with experiment, where the renormalization of X0 by intervalley plasmons yields a stronger blueshift in MoSe2 than in WSe2 due to differences in their band ordering. © 2019 American Physical Society.