Magnetic tunnel junctions (MTJs), ferroelectric/antiferroelectric tunnel junctions (FTJs/AFTJs), and multiferroic tunnel junctions (MFTJs) have recently attracted significant interest for technological applications of nanoscale memory devices. Until now, most of them are based on perovskite oxide heterostructures with a relatively high resistance-area (RA) product and low resistance difference unfavorable for practical applications. The recent discovery of the two-dimensional (2D) van der Waals (vdW) ferroelectric (FE) and magnetic materials has opened a new route to realize tunnel junctions with high performance and atomic-scale dimensions. Here, using first-principles calculations, we propose a new type of 2D tunnel junction: an antiferroelectric magnetic tunnel junction (AFMTJ), which inherits the features of both MTJ and AFTJ. This AFMTJ is composed of monolayer CuInPS (CIPS) sandwiched between 2D magnetic electrodes of CrSe. The AFTJ with nonmagnetic electrodes of TiSe on both sides of CIPS and the asymmetric AFTJ with both CrSe and TiSe electrodes are also investigated. Based on quantum-mechanical modeling of the electronic transport, sizeable tunneling electroresistance effects and multiple nonvolatile resistance states are demonstrated. More importantly, a remarkably low RA product (less than 0.1 Ω·μm) makes the proposed vdW AFMTJs superior to the conventional MFTJs in terms of their promising nonvolatile memory applications. Our calculations provide new guidance for the experiment and application of nanoscale memory devices.