We present a variational message passing (VMP)-based approach to detect the presence of a person based on their respiratory chest motion using multistatic ultra-wideband (UWB) radar. In the process, the respiratory motion is estimated for contact-free vital sign monitoring. The received signal is modeled as a backscatter channel and the respiratory motion and propagation channels are estimated using VMP. We use the evidence lower bound (ELBO) to approximate the model evidence for the detection. Numerical analyses and measurements demonstrate that the proposed method leads to a significant improvement in the detection performance compared to a fast Fourier transform (FFT)-based detector or an estimator-correlator in low-signal-to-noise ratio (SNR) conditions, since the multipath components (MPCs) are better incorporated into the detection procedure. Specifically, the proposed method has a detection probability of 0.95 at −20 dB SNR, while the estimator-correlator and FFT-based detector have 0.32 and 0.05, respectively.