Urbanization drives the epidemiology of infectious diseases to many threats and new challenges. In this research, we study the interplay between human mobility and dengue outbreaks in the complex urban environment of the city-state of Singapore. We integrate both stylized and mobile phone data-driven mobility patterns in an agent-based transmission model in which humans and mosquitoes are represented as agents that go through the epidemic states of dengue. We monitor with numerical simulations the system-level response to the epidemic by comparing our results with the observed cases reported during the 2013 and 2014 outbreaks. Our results show that human mobility is a major factor in the spread of vector-borne diseases such as dengue even on the short scale corresponding to intra-city distances. We finally discuss the advantages and the limits of mobile phone data and potential alternatives for assessing valuable mobility patterns for modeling vector-borne diseases outbreaks in cities.