Its mother was among the first group of 20 relocated to mid Wales from Scotland in 2015.
Pine martens were once common in Wales but were thought to be close to extinction by the 20th Century.
"Evidence of breeding in Wales is very exciting," said Hilary Macmillan from the Vincent Wildlife Trust, a mammal conservation charity.
"This is proving that they are breeding successfully in Wales."
The mother of the baby pine marten - also known as a kit - gave birth about a month ago, must have bred while in Wales to have become pregnant last year.
Others among the relocated group gave birth last year but they would have become pregnant after mating prior to their move south.
However, not everyone is please to see the animals return, with one landowner in Ceredigion dubbing the predator a "killing machine".
So far, 39 pine martens have been relocated to mid Wales in the last two years with a further 20 expected this autumn.
The kit was filmed by trust volunteer Huw Denman as it climbed a tree at its den site.
The first pine marten born and bred in Wales as part of a recovery project has been caught on camera.