Answer: As many people do not realize mushrooms are not plants, this question is quite common. The answer is no, mushrooms do not have roots.
More About Mycelium
In plant terms, the mycelium is the root structure and the mushroom is the flower (all though it is called the fruiting body). When a spore lands in a suitable environment, it germinates from a single meristematic cell.
Mycelium itself consists of the growing ‘stem’ cells of the fungus. As fungi are heterotrophic, they obtain energy from their environment by releasing enzymes from the hyphal tips of the mycelium to digest the surroundings and absorbing the available nutrients.
The mycelium cells branch to grow to build a vast network of mycelial filamentous network.
The mycelium of psychedelic mushroom specs is sold commercially as magic truffles.