In vivo wireless nanosensor networks (iWNSNs) are paving the way toward transformative healthcare solutions. These networks are expected to enable a plethora of applications, including drug-delivery, bio-sensing, and health monitoring. With the development of miniature plasmonic signal sources, antennas, and detectors, wireless communications among intrabody nanodevices will expectedly be enabled in the terahertz (THz) frequency band (0.1-10 THz). Several propagation models were recently developed to analyze and assess the feasibility of intra-body electromagnetic (EM) nanoscale communication. The emphasis of these works has mainly been on understanding the propagation of EM signals through biological media, with limited focus on the intra-body noise sources and their impact on the system performance. In this paper, a stochastic noise model for iWNSNs is presented in which the individual noise sources that impact intra-body systems operating in the THz frequency band are analyzed. The overall noise contributions are composed of three distinctive constituents, namely, Johnson-Nyquist noise, black-body noise, and Doppler-shift-induced noise. The probability distribution of each noise component is derived, and a comprehensive analytical approach is developed to obtain the total noise power-spectral density. The model is further validated via 2-D particle simulations as the active transport motion of particles is conveyed in the presented framework. The developed models serve as the starting point for a rigorous end-to-end channel model that enables the proper estimation of data rate, channel capacity, and other key parameters, which are all factors of the noise environment.