The human glycophorin gene cluster on chromosome 4 encodes two red blood cell surface receptors for Plasmodium falciparum, and variation in these genes also underlies the diverse MNS blood group system. Nearby signals have recently been identified in genome-wide scans for both severe malaria susceptibility and ancient balancing selection, but further insight into underlying functional mechanisms is hindered by the homology between the glycophorin genes. The high level of sequence similarity makes read mapping and variant calling problematic, yet also predisposes the region to frequent non-allelic homologous recombination that leads to structural variation. To identify such variants, we developed a hidden Markov model that is robust to this homology to infer copy number changes from sequence coverage data. We apply the method to worldwide sequence data from 2596 individuals, including 1046 from sub-Saharan Africa. This analysis reveals multiple large deletions and duplications, corresponding both to known blood groups and novel variation. In addition to whole gene duplications and deletions, several are predicted to carry hybrid glycophorin genes. We further consider the possible functional consequences at the red blood cell surface and potential for genetic interactions with variation in the corresponding parasite binding partners.