Preeclampsia (PE) is the serious obstetric-related disease characterized by newly onset hypertension and causes damage to the kidneys, brain, liver, and more. To investigate genes with key roles in PE’s pathogenesis and their contributions, we used a microarray dataset of normotensive and PE patients and conducted a weighted gene co-expression network analysis (WGCNA). Cyan and magenta modules that are highly enriched with differentially expressed genes (DEGs) were revealed. By using the molecular complex detection (MCODE) algorithm, we identified five significant clusters in the cyan module protein–protein interaction (PPI) network and nine significant clusters in the magenta module PPI network. Our analyses indicated that (i) human accelerated region (HAR) genes are enriched in the magenta-associated C6 cluster, and (ii) positive selection (PS) genes are enriched in the cyan-associated C3 and C5 clusters. We propose these enriched HAR and PS genes, i.e., EIF4E, EIF5, EIF3M, DDX17, SRSF11, PSPC1, SUMO1, CAPZA1, PSMD14, and MNAT1, including highly connected hub genes, HNRNPA1, RBMX, PRKDC, and RANBP2, as candidate key genes for PE’s pathogenesis. A further clarification of the functions of these PPI clusters and key enriched genes will contribute to the discovery of diagnostic biomarkers for PE and therapeutic intervention targets.