Intra-crystalline defects in metal-organic frameworks (MOFs) are known to have crucial roles in dictating their material properties. In this work, computational simulations were used to induce linker vacancy defects in MOF membranes and to investigate theirinfluence on $H_2/CH_4$ separation. Linker defective structures were created for the 228 candidate MOFs and their separation performances were compared between the defective and the non-defective structures. Our results show that the existence of linker vacancy defects can lead to significant performance changes in the MOF membranes and more importantly, the ranking of the best materials can differ with the defects present. This suggests the importance of taking into account the potential for defects when it comes to materials design for various membrane separation applications.