Human mobility plays a key role in the dissemination of infectious diseases around the world. However, the complexity introduced by commuting patterns in the daily life of cities makes such a role unclear, especially at the intracity scale. Here, we propose a multiplex network fed with 9 months of mobility data with more than 107 million public bus validations in order to understand the relation between urban mobility and the spreading of COVID-19 within a large city, namely, Fortaleza in the northeast of Brazil. Our results suggest that the shortest bus rides in Fortaleza changed ≈ 25% more than the longest ones after an epidemic wave. Such a result is the opposite of what has been observed at the intercity scale. We also find that mobility changes among the neighborhoods are synchronous and geographically homogeneous. Furthermore, we find that the most central neighborhoods in mobility are the primary targets for infectious disease outbreaks, which is quantified here in terms of the linear relation between the disease arrival time and the average of the closeness centrality ranking. These central neighborhoods are also the top neighborhoods in the number of reported cases at the end of an epidemic wave as indicated by the exponential decay behavior of the disease arrival time in relation to the number of accumulated reported cases with decay constant λ ≈ 33 days. We believe that these results can help in the development of new strategies to impose restriction measures in the cities guiding decision-makers with smart actions in public health policies, as well as supporting future research on urban mobility and epidemiology.