Zika virus (ZIKV) is an arbovirus belonging to the genus Flavivirus (Flaviviridae). ZIKV infection is associated with alterations in various organs, including the liver, lungs, and kidneys. Studies on the influence of posttranscriptional control on viral infections have demonstrated that microRNAs (miRNAs) interfere with different stages of the replicative cycle of several viruses and may influence the disease outcome. To shed light on ZIKV-induced regulation of host miRNA-processing machinery in the above organs, we analyzed the expression of genes encoding key proteins of the miRNA pathway in different ZIKV-infected continuous primate cell lineages (HepG2, A549, and MA104) by reverse-transcription quantitative polymerase chain reaction (RT-qPCR). Expression of the genes encoding the miRNA-related proteins DGCR8, Ago1, and Ago3 in HepG2 cells and Drosha, Dicer, Ago2, and Ago3 in A549 and MA104 cells was significantly altered in the presence of ZIKV. Our results suggest that ZIKV modulates miRNA levels during infection in liver, lung, and kidney cells, which may be an additional mechanism of host cell subversion in these organs.