Characterizing the taxi travel network is of fundamental importance to our understanding of urban mobility, and could provide intellectual support for urban planning, traffic congestion, and even the spread of diseases. However, the research on the interaction network between urban functional area (UFA) units are limited and worthy of notice. Therefore, this study has applied the taxi big data to construct a travel flow network for the exploration of spatial interaction relationships between different UFA units in Shenzhen, China. Our results suggested that taxi travel behavior was more active in UFA units dominated by functions, including residential, commercial, scenic, and greenspace during weekends, while more active in UFA units dominated by industrial function during weekdays. In terms of daily average volume, the characteristics of spatial interaction between the various UFA types during weekdays and weekends were similar. During the morning peak period, the sink areas were mainly distributed in Futian District and Nanshan District, while during the evening peak period, the sink areas were mainly distributed in the southern part of Yantian District, the southwestern part of Longgang District, and the eastern part of Luohu District. The average daily taxi mobility network during weekdays showed a spatial pattern of “dense in the west and north, sparse in the south and east”, exhibiting significant spatial unevenness. Compared with weekdays, the daily taxi mobility network during weekends was more dispersed and the differences in node sizes decreased, indicating that taxi travel destinations were more diverse. The pattern of communities was more consistent with the administrative division during weekdays, indicating that taxi trips are predominantly within the districts. Compared with weekdays, the community pattern of network during weekends was clearly different and more in line with the characteristics of a small world network. The findings can provide a better understanding of urban mobility characteristics in Shenzhen, and provide a reference for urban transportation planning and management.