The cyber and hardware security of constrained edge nodes have become a paramount requirement for the ultimate success of the Internet of Things (IoT). Such security needs to be guaranteed at minimum impact on energy efficiency and autonomy. One important approach to IoT energy autonmoy is the use of energy harvesters. In this paper, we select MEMS piezolelectric energy harvesters to propose a physically unclonable function (Piezo-PUF) which relies on the manufacturing uncertainties of the MEMS fabrication process. The major result of this paper is that several of the MEMS manufacturing uncertainties cannot be easily cloned, which leads to various mechanical and electrical features that can be leveraged for generating cryptographic keys. Thorough security analysis of Piezo-PUF has been conducted using wafer-level simulations and measurements. The security analysis confirms that Piezo-PUF qualifies as weak PUF for secure key generation and authentication.