Auditory object analysis requires the fundamental perceptual process of detecting boundaries between auditory objects. However, the dynamics underlying the identification of discontinuities at object boundaries are not well understood. Here, we employed a synthetic stimulus composed of frequency-modulated ramps known as 'acoustic textures', where boundaries were created by changing the underlying spectrotemporal statistics. We collected magnetoencephalographic (MEG) data from human volunteers and observed a slow (<1 Hz) post-boundary drift in the neuromagnetic signal. The response evoking this drift signal was source localised close to Heschl's gyrus (HG) bilaterally, which is in agreement with a previous functional magnetic resonance imaging (fMRI) study that found HG to be involved in the detection of similar auditory object boundaries. Time-frequency analysis demonstrated suppression in alpha and beta bands that occurred after the drift signal.