Gorka, a member of the endangered westland lowland gorilla species, gave birth to the 1.5kg (3.3lb) baby, her fourth, after a complication-free eighth-month pregnancy.
"Both mother and child are doing well but we still don't know the sex of the baby because Gorka is always cradling it in her lap," María José Luis of the zoo's communications department told The Local.
Zoo staff are now keeping a close eye on the pair, who will likely remain separated from the other five gorillas at the institution for the first month so that mother and child can bond.
A name for the young gorilla will be chosen via the zoo's official Facebook page.
The gorilla was born as part of the important European Endangered Species Programme.