Without a vaccine, the fight against the spreading of the coronavirus has focused on maintaining physical distance. To study the impact of such measures on inter-municipality traffic, we analyze a mobile dataset with the daily flow of people in Portugal in March and April 2020. We find that the reduction in inter-municipality traffic depends strongly on its initial outflow. In municipalities where the mobility is low, the outflow reduced by 10-20% and this decrease was independent of the population size. Whereas, for municipalities of high mobility, the reduction was a monotonic increasing function of the population size and it even exceeded 60% for the largest municipalities. As a consequence of such heterogeneities, there were significant structural changes on the most probable paths for the spreading of the virus, which must be considered when modeling the impact of control measures.