The growth hormone receptor (GHR) is a member of the cytokine/hematopoietic factor receptor superfamily, which plays an important role in the growth and development, immunity, and metabolism of animals. This study identified a 246 bp deletion variant in the intronic region of the GHR gene, and three genotypes, including type II, type ID, and type DD, were observed. Genotype analysis of structural variation (SV) was performed on 585 individuals from 14 yak breeds, and it was found that 246 bp deletion was present in each breed. The II genotype was dominant in all yak breeds except for SB yak. The association analysis of gene polymorphisms and growth traits in the ASD yak population showed that the 246 bp SV was significantly associated with body length at 6 months (p < 0.05). GHR messenger RNA (mRNA) was expressed in all the tested tissues, with significantly higher levels in the liver, muscle, and fat than in other organs. The results of transcription activity showed that the luciferase activity of the pGL4.10-DD vector was significantly higher than that of the pGL4.10-II vector (p < 0.05). Additionally, the transcription-factor binding prediction results showed that the SV in the runt-related transcription factor 1 (Runx1) transcription-factor binding site may affect the transcriptional activity of the GHR gene, regulating yak growth and development. This study showed that the novel SV of the GHR gene could be used as a candidate molecular marker for the selection of the early growth trait in ASD yak.