This is a very good question, and a good one for a debate.
Management, as a field of study, is often classified as a science. The reason for it is because the field involves and requires enough research to identify which are the best practices to conduct within an organization in a leadership position.
Another reason why it is classified as a science is because there is a specific methodology involved in the process of hiring, firing, limiting, modifying, and implementing both personnel and new programs. Usually the methodology that is required to manage a small or a large corporation is quite clear-cut and repetitive. This alone may qualify it as a science.
However, it is arguable that Management requires art in the form of visibility, marketing, symbolism (logos, mottoes, tag lines), not to mention the need for creative ways to empower and motivate employees. All this involves artistry, charm, and charisma: Those latter elements are hardly scientific, but are just as effective as the elements that are.
In all, management is a combination of leadership, research, and productivity. In turn, a successful result can only be possible with a combination of research-based best practices and the inclusion of artistic features such as good marketing, attractive symbolism, and high visibility.