No, Jupiter is a planet not a star. Brown dwarfs start out well over a dozen times more massive than Jupiter. Planets form from a proto-planetary disk, as Jupiter did (you can tell because it is in the same orbital plane as the other planets, the same as the original plane of the disk).

99.9% the mass of the Solar System is in the Sun. 0.1% of the mass of the Solar System is in Jupiter. It's very big for a planet in our Solar System but it is very small compared to even the smallest stars.