The meme-inspired cryptocurrency has a total value of over US$80 billion.
The Tesla CEO has been a vocal proponent of cryptocurrencies.
She tweeted she was "purring like a bobcat rolling in catnip" because of the coin's popularity.
The move comes after a digital artwork was sold for $US70m by Christies.
Qoin has suffered backlash in Australia, with concerns raised about the transparency of its dealings.
Pyramid schemes are illegal under the Fair Trading Act.
The cryptocurrency hit fresh record highs of US$41,530 on Friday.
It encourages people to pay hundreds of dollars to join the scheme.
What it is, how to use it, how it can help you.