Car dependence has been threatening transportation sustainability as it contributes to congestion and associated externalities. In response, various transport policies that restrict the use of private vehicle have been implemented. However, empirical evaluations of such policies have been limited. To assess these policies' benefits and costs, it is imperative to accurately evaluate how such policies affect traffic conditions. In this study, we compile a refined spatio-temporal resolution data set of the floating-vehicle-based traffic performance index to examine the effects of a recent nonlocal vehicle driving restriction policy in Shanghai, one of most populous cities in the world. Specifically, we explore whether and how the policy impacted traffic speeds in the short term by employing a quasi-experimental difference-in-differences modeling approach. We find that: (1) In the first month, the policy led to an increase of the network-level traffic speed by 1.47% (0.352 km/h) during evening peak hours (17:00-19:00) but had no significant effects during morning peak hours (7:00-9:00). (2) The policy also helped improve the network-level traffic speed in some unrestricted hours (6:00, 12:00, 14:00, and 20:00) although the impact was marginal. (3) The short-term effects of the policy exhibited heterogeneity across traffic analysis zones. The lower the metro station density, the greater the effects were. We conclude that driving restrictions for non-local vehicles alone may not significantly reduce congestion, and their effects can differ both temporally and spatially. However, they can have potential side effects such as increased purchase and usage of new energy vehicles, owners of which can obtain a local license plate of Shanghai for free.