I assume you intend the problem in which the polygon's vertices must be exactly the given set of points. If so, then, Yes, the problem is NP-hard:
Fekete, Sándor P. "On simple polygonalizations with optimal area." Discrete & Computational Geometry 23.1 (2000): 73-110. (Journal link.)
![Fig1a][1]
Approximation algorithms have been explored:
Taranilla, María Teresa, Edilma Olinda Gagliardi, and Gregorio Hernández Peñalver. "Approaching minimum area polygonization." (2011): 161-170. (Authors' link.)
The key search term for this problem is polygonization.