Monsters are not affected by Solemn Judgment unless their effects are activated on the field. For example, if a monster's effect is to destroy a card on the field when it is Summoned, Solemn Judgment can be activated to negate the activation of the monster's effect and destroy it. However, if a monster's effect does not activate on the field, such as an effect that allows the player to draw a card when they take damage, Solemn Judgment cannot be activated to negate it.
In summary, Solemn Judgment can only negate the activation of Spell, Trap, or Monster Cards on the field. It cannot negate the effects of monsters that do not activate on the field.