No, the Unity engine is not owned by Ubisoft. Unity Technologies is the creator and owner of the Unity engine. It was founded by David Helgason, Joachim Ante, and Nicholas Francis in Denmark in 2004. Unity Technologies is an independent company that has no ownership ties to Ubisoft.
Ubisoft is a French video game company known for creating popular franchises such as Assassin's Creed, Far Cry, and Just Dance. While Ubisoft does use various engines for their games, including their proprietary engines like Anvil and Snowdrop, they do not own the Unity engine.
It's worth noting that Unity Technologies went public on the New York Stock Exchange in September 2020 under the ticker symbol "U". This initial public offering further established Unity Technologies as an independent entity with a diverse pool of shareholders, rather than being owned by any single corporation, including Ubisoft.