Orys, a male calf, was born after a 492-day pregnancy to mother Quetta late on Saturday night, weighing a hefty 68kg, said the zoo.
After a healthy birth he got up on his wobbly legs around an hour later, it said.
Orys is the 35th Indian rhinoceros born at the zoo since 1956, when its first, Rudra, became the first baby Indian rhino to be born in captivity anywhere in the world.
Since 1972 the zoo has been coordinating the international breeding register for Indian rhinos as well as a European breeding programme.
Photo: Basel Zoo
Like most species of rhinos, the Indian rhinoceros is threatened in the wild, with many killed by poachers for their horns.
Nearly 1,200 were killed in that way in 2015, said the zoo, with only 3,400 still left in the wild.
After remaining shut for several days, the enclosure housing baby Orys and mother Quetta is now open for public viewing most of the day.
Basel zoo is also home to Saar, a 17-year-old rhino, and bull Jaffna, father of Orys.
Watch Orys take his baby steps here: