Zookeepers were delighted by the exotic new arrival and put out an appeal for names - but were overwhelmed by the more than 1,500 ideas which were sent in from across the globe.
Staff have filled the eastern German zoo's Facebook page with pictures of the little male tapir, attracting hundreds of comments and name suggestions.
Fewer tapirs are being born in captivity than ever before and in the wild they are being threatened with extinction, said zoo director Jörg Junhold.
The animals are most closely related to horses and rhinos, while their noses and upper lips form a prehensile snout a little like an elephant's nose. They communicate with high-pitched, screechy whistles and eat aquatic plants as well as fallen fruit.
Possible names for the new Leipzig tapir include Tapsi, Flecki or Dot – inspired by the tapir baby's spotty fur which in around six month's time will give way to a darker, plain pelt.
But the change in the animal's colouring made it difficult to pick a name related to the early pattern said Junhold. “The name has to fit for the tapir's whole life,” he said. Leipzig zoo considers its animals to be ambassadors for their species in the wild, he added.
Tapirs originate in Southeast Asia, meaning that zoo staff may well opt for a more geographically appropriate name. Bintang, Malayan for star, or Tenuk, for tapir, are both also being considered.
Deadline for suggestions was initially March 18th but the zoo has extended it to March 27th, due to the excitement from tapir fans worldwide that the birth has generated.
“People are really making an effort, like researching the meaning of names on the internet,” said Junhold.
Leipzig zoo has been in the limelight since Heidi the cross-eyed possum became a celebrity in 2011, gaining fame for predicting that year's Oscar nominations. She died last year along with her sister and three others, signalling the end of the zoo's possum enclosure.