I assume "the world" means Earth. It is likely that somewhere in the universe where a supernova (or a neutron star merger, see comment) has recently occurred during which the r-process prevailed, plutonium can be found.
First, note that the most stable isotope of plutonium (Pu-244) has a half-life of about 81 million years, whereas the Earth is about 4540 million years old. From this it follows that there is no primordial plutonium left on Earth. When Earth was very young, it probably existed, but all that has decayed by now.
As explained by DJohnM's answer, at least once in the natural history of our planet, plutonium was produced in a so-called natural fission reactor in Oklo, Gabon. However, the plutonium produced by these natural processes on Earth will have decayed by now. Because the ratio between uranium-235 and uranium-238 has been gradually changing, natural fission reactors cannot have occurred in "recent" times, so it is impossible that plutonium from natural reactors still exists today.
So the claim is largely correct. While uranium is a primordial element on Earth, discovered in 1789, plutonium is not naturally abundant.
However, to be precise, we have to define more precisely what we mean by "an element existing" in the world. It will happen by accident once in a while that one uranium nucleus fissions (spontaneously), producing neutrons one of which is slowed down and hits another uranium nucleus, producing the heavier uranium-239. After two beta decays, the latter turns into plutonium-239. Pu-239 has a half-life of about 0.024 million years. All this means that wherever U-238 exists, these nuclear processes will reach an equilibrium, and there will be an absolutely tiny trace amount of plutonium present. That is the 10-11 fraction mentioned in Jan Doggen's answer.
It is debatable whether one part plutonium in 100 billion parts uranium qualifies as "plutonium existing in the world". One thing is certain: It is not practically possible to mine or extract plutonium from such sparse occurrences. This is important in politics when we want to limit the proliferation of nuclear weapons; the only feasible way to obtain plutonium is from access to nuclear reactor technology.
We can illustrate how tiny 10-11 is by comparing the natural trace occurrence of plutonium to the amount of plutonium spread by the detonation of nuclear weapons since 1945. These two sources are comparable. In other words, if you encounter a plutonium atom in nature, it is at least as like to originate from one of the nuclear weapons used or tested since 1945, as to be of natural origin.