Hybrid breeding is an efficient system to break the yield barriers in many crops. For an effective hybrid seed production, a pool of male parental lines with appropriate anther extrusion (AE) ensuring pollen shedding outside the florets for efficient cross fertilization is required. We investigated the genetic architecture of AE using genome-wide association studies (GWAS) and examined the potential of genome-wide prediction (GP) for AE based on a panel of 309 CIMMYT spring wheat lines evaluated in field trials and fingerprinted with genotyping-by-sequencing. The broad-sense heritability of AE was 0.64. Genotypic data consisted of 14,921 polymorphic markers. GWAS discovered no significant marker at FDR (P) ≤ 0.20, suggesting that this trait is controlled by many small effect loci. Average accuracy of ridge-regression best linear unbiased prediction was 0.62. We conclude that GP is a suitable method to select for AE, which is otherwise challenging to phenotype.