Mouse deer, also known as Chevrotain, are native to Southeast Asia and when fully grown are 22 inches in length and weigh less than 5 pounds.
The deer stood by itself moments after being born Tuesday, officials at the Parken Zoo said.
"It's absolutely beautiful," zoo Director Helena Olsson told The Local.se.
"It's so small and charming -- even when they're fully grown they're still tiny, tiny, tiny!"
The marks the zoo's first success in their attempts to preserve the future of the species, she said.
"We're all very happy that its parents, Musse, 1, and Mimmi, 2, liked each other and mated as soon as they were put together."
Determining the baby's sex will take a while, she said.
"Since mouse deer are very protective and as we want to respect their privacy at all costs, we won't know what gender it is for a few months."