Zika virus (ZIKV) is a member of the Flaviviridae family causing asymptomatic or mildly symptomatic infections with fever, rash, arthralgia and headache. It is transmitted by the Aedes species mosquitoes and also sexually and transplacentally, and has been recently associated with congenital neurologic birth defects in South and Central America. We report the case of a newly married couple from Greece who travelled to Cuba for their honeymoon and developed mild symptoms consistent with arboviral infection. After returning to Greece, they were found to have been infected by Zika virus during their honeymoon. These are the first two cases of Zika virus infection in Greece, the southeastern border of Europe, denoting that Zika virus infection poses a threat for public health worldwide, since returning travelers could be asymptomatic carriers of the virus, not only leading to risk of neurologic birth defects for their offspring but also the real risk of transmission of the virus in their country by local Aedes mosquitoes.