Zika virus (ZIKV) is a Flavivirus that is transmitted to humans by Aedes mosquitoes. ZIKV is divided into two phylogenetic lineages, African and Asian. In the Asian lineage, Pacific and American clades have been linked to the recent worldwide outbreak of ZIKV. The aim of this study was to measure the vector competence of Aedes aegypti for seven ZIKV strains belonging to both lineages. We demonstrate that Ae. aegypti from New Caledonia (NC), South Pacific region, is a low-competence vector for Asian ZIKV (<10% transmission efficiency). No significant differences were observed in vector competence with respect to the sampling date and collection site of Asian ZIKV strains used (2014 and 2015 for New Caledonia, Pacific clade, and 2016 for French Guiana, American clade). The ability of the New Caledonian Ae. aegypti to transmit ZIKV is significantly greater for the earlier viral isolates belonging to the African lineage (>37% transmission efficiency after 9 days post-infection) compared to recent ZIKV isolates from African (10% transmission efficiency) and Asian lineages (<10% transmission efficiency). The results of this study demonstrate that Ae. aegypti from NC can become infected and replicate different ZIKV strains belonging to all lineages. Our data emphasize the importance of studying the interaction between vectors and their arboviruses according to each local geographic context. This approach will improve our understanding of arbovirus transmission to prevent their emergence and improve health surveillance.