It has been shown that the processing of time activates a spatial left-to-right mental timeline, where past events are “located” to the left and future events to the right. If temporal information conveyed by words also activate this mental timeline, then the processing of such words should interfere with hand movements that go in the opposite direction (e.g., leftwards for future words, rightwards for past words). To test this hypothesis, we conducted three visual lexical decision tasks with conjugated (past/future) verbs and pseudo-verbs. In Experiment 1, participants moved a pen to the right or left of a trackpad to indicate whether a visual stimulus was a real word or not. In the congruent condition, grammatical time and hand movements for yes responses went in the same direction (e.g., past tense/leftward movement). In the incongruent condition, grammatical time and hand movements for yes responses went in opposite directions. Analyses showed that space-time incongruency significantly slowed down movements (i.e., reaction times) and increased error rates. In Experiment 2, we investigated the role of movement in this language-driven space-time congruency effect. Participants performed the same lexical decision task by responding either with a trackpad (movement), a mouse (movement) or a keyboard (no movement). The results of Experiment 2 replicated the congruency effect of Experiment 1, but only when the decision required a movement. In Experiments 1 and 2, conjugated verbs and pseudo-verbs were preceded by a temporal prime (yesterday or tomorrow). In Experiment 3, we investigated the role of those primes in the space-time congruency effect. Participants performed the same lexical decision task by responding with a trackpad (movement) but no prime was used. The results of Experiment 3 showed that the space-time congruency effect does not require temporal word priming. Altogether, these results suggest an automatic activation of a left-right mental timeline during word recognition, reinforcing the claim that the abstract concept of time convey by conjugated-verbs is grounded in movement through space.