Nope, says reddit.com.
It has several key characteristics of Communism, most notably elimination of property, profit, business and money. Replicators handle “to each according to his ability.”
But the Federation fails one characteristic of Communism: Eliminating government.
Star Trek under Roddenberry hated business, particularly in “The Next Generation.” But Roddenberry himself was a businessman. As portrayed in These Are the Voyages, Roddenberry’s ego made him self-sabotaging. He blamed others, and was reluctant to share credit and profit. He was kind of a Ferengi, actually.