Background Since the major outbreak in 2007 in the Yap Island, Zika virus (ZIKV) causing dengue-like syndromes has affected multiple islands of the South Pacific region. In May 2015, the virus was detected in Brazil and then spread through South and Central America. In December 2015, ZIKV was detected in French Guiana and Martinique. The aim of the study was to evaluate the vector competence of the mosquito spp. Aedes aegypti and Aedes albopictus from the Caribbean (Martinique, Guadeloupe), North America (southern United States), South America (Brazil, French Guiana) for the currently circulating Asian genotype of ZIKV isolated from a patient in April 2014 in New Caledonia. Methodology/Principal Findings Mosquitoes were orally exposed to an Asian genotype of ZIKV (NC-2014-5132). Upon exposure, engorged mosquitoes were maintained at 28°±1°C, a 16h:8h light:dark cycle and 80% humidity. 25–30 mosquitoes were processed at 4, 7 and 14 days post-infection (dpi). Mosquito bodies (thorax and abdomen), heads and saliva were analyzed to measure infection, dissemination and transmission, respectively. High infection but lower disseminated infection and transmission rates were observed for both Ae. aegypti and Ae. albopictus. Ae. aegypti populations from Guadeloupe and French Guiana exhibited a higher dissemination of ZIKV than the other Ae. aegypti populations examined. Transmission of ZIKV was observed in both mosquito species at 14 dpi but at a low level.Conclusions/Significance This study suggests that although susceptible to infection, Ae. aegypti and Ae. albopictus were unexpectedly low competent vectors for ZIKV. This may suggest that other factors such as the large naïve population for ZIKV and the high densities of human-biting mosquitoes contribute to the rapid spread of ZIKV during the current outbreak.