Encroachment by woody invasive plants is a major threat to grasslands and savannah ecosystems worldwide. Rodents, being primary consumers, are likely to be the first to respond to changes in the structure and composition of native vegetation. We examined the effect of an invasive shrub Prosopis juliflora (hereafter Prosopis) on the native rodent community of an arid grassland system of Western India. Our sampling plots were divided into five categories representing different stages of Prosopis invasion and other land cover types. These consisted of restored native grassland, agriculture fallow, open brushland, sparse-Prosopis plots, and Prosopis-dominated plots. We also examined the impact of woody invasion on the response of native rodents toward moonlight and temperature. As hypothesized, we found a significantly higher abundance of rodent species in the native grassland habitat compared to sparse-Prosopis habitats. However, there was no significant difference in rodent abundance and diversity between the grassland and Prosopis-dominated habitats. Thus, species richness and abundance of rodents were the highest in the restored grasslands and dense Prosopis thickets, and the lowest in the sparse Prosopis, potentially showing a “U” shaped response to Prosopis invasion. We observed a species-specific effect of Prosopis on the activity of Tatera indica, Bandicota bengalensis, and Millardia meltada. Habitat type mediated the effect of different environmental factors (moonlight and temperature) on the activity of the most commonly ocurring species T. indica while activity of M. meltada showed a weak association with environmental factors. B. bengalensis was the most generalist species showing similar activity across all habitat types. Thus, the impact of Prosopis invasion on the rodent community was uneven, and depended on species as well as on local environmental characteristics.