HER2-positive breast cancer (BC) is an aggressive subtype that affects 20–25% of BC patients. For these patients, neoadjuvant therapy is a good option that targets a pathological complete response (pCR) and more breast-conserving surgery. In effect, the outcomes of patients with HER2-positive BC have dramatically improved since the introduction of anti-HER2 antibodies such as trastuzumab (TZ) and/or pertuzumab (PZ) added to chemotherapy. This study sought to examine whether correlation exists between copy number variations (CNVs) in several genes related to the PI3K/AKT pathway (HER2, FGFR1, PIK3CA, AKT3 and MDM2) and the efficacy of anti-HER2 neoadjuvant treatment in patients with early HER2-positive BC. Forty-nine patients received TZ or PZ/TZ and chemotherapy as neoadjuvant treatment. Gene CNVs were determined by quantitative polymerase chain reaction on paraffin-embedded biopsy specimens. The response to 6 months of therapy was assessed by Miller–Payne grading of the tumor on surgical resection; grades 4 and 5, indicating >90% tumor reduction, were defined as a good response. A good response was shown by 64.5% and a pCR by 31.2% of patients. When stratified by anti-HER2 antibody received and gene CNV, it was found that patients with FGFR1 gene amplification or those with FGFR1 amplification treated with TZ alone showed a poor response (p = 0.024 and p = 0.037, respectively). In the subset of patients treated with TZ/PZ combined, the pCR rate was significantly lower among those showing FGFR1 amplification (p = 0.021). Although based on a small sample size, our findings suggest that patients with FGFR1 amplification might benefit less from anti-HER2 antibody therapy.