In fifth generation (5G) new radio (NR), the demodulation reference signal (DMRS) is employed for channel estimation as part of coherent demodulation of the physical uplink shared channel. However, DMRS spoofing poses a serious threat to 5G NR since inaccurate channel estimation will severely degrade the decoding performance. In this correspondence, we propose to exploit the spatial sparsity structure of the channel to detect the DMRS spoofing, which is motivated by the fact that the spatial sparsity structure of the channel will be significantly impacted if the DMRS spoofing happens. We first extract the spatial sparsity structure of the channel by solving a sparse feature retrieval problem, then propose a sequential sparsity structure anomaly detection method to detect DMRS spoofing. In simulation experiments, we exploit clustered delay line based channel model from 3GPP standards for verifications. Numerical results show that our method outperforms both the subspace dimension based and energy detector based methods.