Multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) cellular network is promising for supporting massive connectivity. This paper exploits low-latency machine learning in the MIMO-NOMA uplink transmission environment, where a substantial amount of data must be uploaded from multiple data sources to a one-hop away edge server for machine learning. A delay-aware edge learning framework with the collaboration of data sources, the edge server, and the base station, referred to as DACEL, is proposed. Based on the delay analysis of DACEL, a NOMA channel allocation algorithm is further designed to minimize the learning delay. The simulation results show that the proposed algorithm outperforms the baseline schemes in terms of learning delay reduction.