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Interactions of quantum materials with strong laser fields can induce exotic non-equilibrium electronic states. Monolayer transition metal dichalcogenides, a new class of direct-gap semiconductors with prominent quantum confinement, offer exceptional opportunities for the Floquet engineering of excitons, which are quasiparticle electron–hole correlated states8. Strong-field driving has the potential to achieve enhanced control of the electronic band structure and thus the possibility of opening a new realm of exciton light–matter interactions. However, a full characterization of strong-field driven exciton dynamics has been difficult. Here we use mid-infrared laser pulses below the optical bandgap to excite monolayer tungsten disulfide and demonstrate strong-field light dressing of excitons in excess of a hundred millielectronvolts. Our high-sensitivity transient absorption spectroscopy further reveals the formation of a virtual absorption feature below the 1s-exciton resonance, which we assign to a light-dressed sideband from the dark 2p-exciton state. Quantum-mechanical simulations substantiate the experimental results and enable us to retrieve real-space movies of the exciton dynamics. This study advances our understanding of the exciton dynamics in the strong-field regime, showing the possibility of harnessing ultrafast, strong-field phenomena in device applications of two-dimensional materials.