Melt butter in a large pot over medium heat. Add onions, carrots, and celery, cooking until they soften. Stir in minced garlic and cook for another minute until fragrant.
Pour in the chicken broth and bring to a boil. Stir in the wild rice, reduce heat to low, and let it simmer for about 30 minutes until the rice is tender.
Add the shredded chicken, salt, and pepper. Stir well and let it simmer for another 10 minutes, allowing the flavors to blend.
Reduce heat to low and slowly stir in the heavy cream. Let the soup cook for another 5 minutes until it becomes thick and creamy. Adjust seasoning if needed.