Shariah urged us to practice sport of all kinds, and there are multiple authentic hadiths indicating that the Messenger of God (peace be upon him) practiced various sports. He encouraged them and organized the occasions for competing in them, whether the sport of shooting arrows or racing, or even between animals, and so on, in order to strengthen the body of a believer. The strong believer is good and beloved to Allah than the weak believer.
Given that bodybuilding tournaments requires the builder to preserve his body and strengthen his structure, which this is required in Shariah; such tournaments are legitimate and competing in them is also legitimate, and giving prizes to those who win them is also legitimate, because it achieves the creation of strong Muslims who maintain their bodies and terrorize God’s enemies and their enemies, which is also legitimately required.