Meiotic recombination is a critical process for plant breeding, as it creates novel allele combinations that can be exploited for crop improvement. In wheat, a complex allohexaploid that has a diploid-like behaviour, meiotic recombination between homoeologous or alien chromosomes is suppressed through the action of several loci. Here, we report positional cloning of Pairing homoeologous 2 (Ph2) and functional validation of the wheat DNA mismatch repair protein MSH7-3D as a key inhibitor of homoeologous recombination, thus solving a half-century-old question. Similar to ph2 mutant phenotype, we show that mutating MSH7-3D induces a substantial increase in homoeologous recombination (up to 5.5 fold) in wheat-wild relative hybrids, which is also associated with a reduction in homologous recombination. These data reveal a role for MSH7-3D in meiotic stabilisation of allopolyploidy and provides an opportunity to improve wheat's genetic diversity through alien gene introgression, a major bottleneck facing crop improvement.