Interaction analysis of GWAS can detect signal that would be ignored by single variant analysis, yet few robust interactions in humans have been detected. Recent work has highlighted interactions in the MHC region between known HLA risk haplotypes for various autoimmune diseases. To better understand the genetic interactions underlying celiac disease (CD), we have conducted exhaustive genome-wide scans for pairwise interactions in five independent CD case-control studies, using a rapid model-free approach to examine over 500 billion SNP pairs in total. We found 14 independent interaction signals within the MHC region that achieved stringent replication criteria across multiple studies and were independent of known CD risk HLA haplotypes. The strongest independent CD interaction signal corresponded to genes in the HLA class III region, in particular PRRC2A and GPANK1/C6orf47, which are known to contain variants for non-Hodgkin's lymphoma and early menopause, co-morbidities of celiac disease. Replicable evidence for statistical interaction outside the MHC was not observed. Both within and between European populations, we observed striking consistency of two-locus models and model distribution. Within the UK population, models of CD based on both interactions and additive single-SNP effects increased explained CD variance by approximately 1% over those of single SNPs. The interactions signal detected across the five cohorts indicates the presence of novel associations in the MHC region that cannot be detected using additive models. Our findings have implications for the determination of genetic architecture and, by extension, the use of human genetics for validation of therapeutic targets.