The child was born by caesarean section at the Vall D'Hebron hospital in Barcelona.
The hospital's chief neonatal physician Felix Castillo confirmed that the baby had been born with a small head circumference, a typical symptom of the Zika virus.
The pregnancy had gone to term, the hospital confirmed.
The baby, which was born by Caesarean section at the end of pregnancy, "is stable and has not required any specific resuscitation," Castillo stated. Obstetrician Elena Carreras said that the mother “had been accompanied by the father the whole time, and they are very excited and happy.”
This is Spain's first case of Zika-related microcephaly, a severe form of brain damage where babies are born with abnormally small heads. The mother had been infected with Zika and dengue during a trip to Latin America.
It is the first known case of its kind in Europe in a baby that has gone to term. Traces of Zika were found in the brain of an aborted foetus in Slovenia that had severe microcephaly.
"The anomalies were identified between the 19th and 20th weeks of pregnancy," a Catalonia health official told reporters in June, confirming that the foetus had shown "several anomalies, including microcephaly".
Authorities declined to identify the woman in order to protect her privacy, but local media said she had decided against an abortion.
"These symptoms cause serious difficulties, but do not usually lead to the death of the foetus," said gynaecologist Elena Carreras.
A total of 105 people in Spain have been infected with the mosquito-borne Zika virus, according to official statistics from May 3.
Spanish authorities have said all the infection cases – including 13 pregnant women – are "imported cases" found in people either "from, or who have visited affected countries" in Latin America.
More than a fifth of foreign residents in Spain are of Latin American or Caribbean origin, the area hit by the epidemic.
The current Zika outbreak began in early 2015 in Brazil, where some 1.5 million infections have been reported. Since then, the epidemic has spread to several other countries in the Americas.
Scientists believe the virus to be responsible for a surge in Brazilian infants born with microcephaly.
There is no vaccine or treatment for the virus, which in most people causes only mild symptoms -- a rash, joint pain or fever.
Despite a flurry of research, very little is known about Zika, including the full list of diseases and disorders it may cause.
Recent scientific consensus is that the virus causes microcephaly in babies and adult-onset neurological problems such as Guillain-Barre Syndrome, which can cause paralysis and death.