For mission-critical massive machine-type communications (mMTC) applications, the messages are required to be delivered in real-time. However, due to the weak security protection capabilities of the low-cost and low-complexity machine-type devices, active jamming attack in the uplink access is a serious threat. Uplink access jamming (UAJ) can increase the number of dropped/retransmitted packets and restrict or prevent the normal device access. To tackle this vital and challenging problem, we propose a novel UAJ detection method based on the joint space-time sparsity (JSTS). Our key insight is that the JSTS-based feature will be significantly impacted if UAJ happens, since only a small fraction of the devices are active and the traffic pattern for each device is sporadic in the normal state. Unlike the existing detection methods under batch mode (i.e., all sample observations are collected before making a decision), the JSTS-based detection is performed in a sequential manner by processing the received signals one by one, which can detect UAJ as quickly as possible. Moreover, the proposed JSTS-based method does not rely on the prior knowledge of the attackers, since it only cares the abrupt change in the JSTS-based feature on each frame. Numerical results evaluate and confirm the effectiveness of our method.