Influenza A virus (IAV) can cause infectious respiratory diseases in humans and animals. IAVs mutate rapidly through antigenic drift and shift, resulting in the emergence of numerous IAV subtypes and significant challenges for IAV detection. Therefore, achieving the simultaneous detection of multiple IAVs is crucial. In this work, three specific aptamers targeting the hemagglutination (HA) protein of the influenza A H5N1, H7N9, and H9N2 viruses were screened using a multichannel magnetic microfluidic chip. The aptamers exhibit nanomolar affinity and excellent specificity for the HA protein of H5N1, H7N9, and H9N2 viruses. Furthermore, three specific aptamers were truncated and labeled with different fluorescence markers to realize fluorescence quantitative detection of influenza A H5N1, H7N9, and H9N2 viruses through an aptamer sandwich assay in 1 h. The limit of detection (LOD) of the developed method is 0.38 TCID50/mL for the H5N1 virus, 0.75 TCID50/mL for the H7N9 virus, and 1.14 TCID50/mL for the H9N2 virus. The detection method has excellent specificity, strong anti-interference ability, and good reproducibility. This work provides a sensitive quantitative detection method for the H5N1, H7N9, and H9N2 viruses, enabling quantitative fluorescence detection for multiple IAV subtypes.