The infection is suspected of causing babies to be born with underdeveloped brains and abnormally small heads if the mother has it during pregnancy.
Children with microcephaly face lifelong difficulties, including intellectual impairment.
It can be fatal. Brazil has been the centre of the current outbreak of the virus.
Carlos Mejia, director of the infectious diseases department at Guatemala City`s Hospital Roosevelt, said two other babies were undergoing tests to determine if their mothers had caught Zika while pregnant.
Zika is commonly transmitted through mosquitoes but can also be transmitted sexually.
The UN estimates says that 20% of women in Guatemala who are sexually active are not using contraception, despite being fertile and not wanting to get pregnant.
Abortion is illegal in Guatemala - it can only be performed to save a mother`s life.
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