Zoo vet Fabia Wyss said the mother was 17-year-old Sumatran orangutan Kila, who came to the zoo along with five other members of her species in 2012, Blick reported.
She said the father was unknown since Kila shares the enclosure with three males, and the zoo would be carrying out a paternity test on the male baby named Ombak.
Wyss described Kila as a real “go-getter” and said she had been very popular with the males.
Ombak's birth at the beginning of March comes four years after that of orangutan Ketawa, who made history as the first to be born at the zoo since 1900.
It is the first baby for Kila, but she does have experience of motherhood having “adopted” her two-year-old sister eight years ago following the death of their mother.
Ombak will be dependent on his mother for six to seven years and learn everything he needs to know from her as orangutans are solitary animals.
Sumatran orangutans are endangered, and have died out in many regions of the Indonesian island.
Only an estimated 14,000 live in the forested north.
Since 2010 Basel zoo has been supporting an orangutan protection project in neighbouring Borneo.