In this work, we present MPIGeneNet, a parallel tool that applies Pearson's correlation and Random Matrix Theory to construct gene co-expression networks. It is based on the state-of-the-art sequential tool RMTGeneNet, which provides networks with high robustness and sensitivity at the expenses of relatively long runtimes for large scale input datasets. MPIGeneNet returns the same results as RMTGeneNet but improves the memory management, reduces the I/O cost, and accelerates the two most computationally demanding steps of co-expression network construction by exploiting the compute capabilities of common multicore CPU clusters. Our performance evaluation on two different systems using three typical input datasets shows that MPIGeneNet is significantly faster than RMTGeneNet. As an example, our tool is up to 175.41 times faster on a cluster with eight nodes, each one containing two 12-core Intel Haswell processors. The source code of MPIGeneNet, as well as a reference manual, are available at https://sourceforge.net/projects/mpigenenet/.