Terahertz (THz) wireless data centers can provide low-latency networks and dynamic scalability that are vital for the next-generation cloud computing infrastructure. The knowledge of THz propagation characteristics in a data center environment is essential to the development of novel THz communication systems. However, a comprehensive characterization and modeling of THz propagation channels, which includes various obstructions in a data center is not available. This paper presents results from a THz channel measurement campaign conducted in a data center environment. Various propagation scenarios such as line-of-sight (LoS) link, non-LoS (NLoS) link using existing materials in a data center to redirect the beam, and obstructed-LoS (OLoS), -NLoS (ONLoS) links with common objects in data centers (cables and server racks’ mesh doors) serving as obstruction were investigated. Propagation channel parameters such as pathloss and root-mean-squared (RMS) delay spread were analyzed in the aforementioned scenarios while cluster-based modeling was implemented for some scenarios. The proposed model for THz propagation in a data center environment was validated with the measured data. The average inter-arrival time of clusters ( $1/\Lambda $ ) and rays ( $1/\lambda $ ) are estimated as 4.4 ns and 0.24 ns, respectively. We find that local scattering objects such as server-rack frames/pillars can be used to assist the NLoS type of link, and that cooling airflow in the data center has a negligible impact on THz propagation. Power cables and mesh doors of the server racks can cause additional attenuation of about 20 dB and 6 dB, respectively. Cluster model and other characterization results provided in this work are pertinent to THz wireless system design for data center environments.