Curiosity is a separate quality from human intelligence, though, in people, they are related. We know this because all mammals have curiosity, and not all have intelligence.
Studies of curiosity indicate that it is the natural, healthy state of all mammals. A lack of curiosity is created by two things: 1) Basic needs not being met (or a perception that they are not being met); or 2) fear.
When people's basic needs are met and we are not afraid, we, like all mammals, go exploring. The urge to explore is curiosity.
In relation to intelligence, curiosity allows the growth of intelligence. Learning, the growth of intelligence, is nearly impossible in a state of fear or desperate need. When we relax from need and fear we become curious. In curiosity, if we turn it outward, we learn more about the world. If we focus on human culture, we learn more about art and society, people and culture. And if we turn it inwards, we can discover ourselves, increase our capabilities, release our limitations, and become truly free.
So, in my view, curiosity is not part of intelligence. It is a separate quality, and a very important one that can enhance our many intelligences.