Accurate and precise identification of adeno-associated virus (AAV) vectors play an important role in dose-dependent gene therapy. Although solid-state nanopore techniques can potentially be used to characterize AAV vectors by capturing ionic current, the existing data analysis techniques fall short of identifying them from their ionic current profiles. Recently introduced machine learning methods such as deep convolutional neural network (CNN), developed for image identification tasks, can be applied for such classification. However, with smaller data set for the problem in hand, it is not possible to train a deep neural network from scratch for accurate classification of AAV vectors. To circumvent this, we applied a pre-trained deep CNN (GoogleNet) model to capture the basic features from ionic current signals and subsequently used fine-tuning-based transfer learning to classify AAV vectors. The proposed method is very generic as it requires minimal preprocessing and does not require any handcrafted features. Our results indicate that fine-tuning-based transfer learning can achieve an average classification accuracy between 90 and 99% in three realizations with a very small standard deviation. Results also indicate that the classification accuracy depends on the applied electric field (across nanopore) and the time frame used for data segmentation. We also found that the fine-tuning of the deep network outperforms feature extraction-based classification for the resistive pulse dataset. To expand the usefulness of the fine-tuning-based transfer learning, we have tested two other pre-trained deep networks (ResNet50 and InceptionV3) for the classification of AAVs. Overall, the fine-tuning-based transfer learning from pre-trained deep networks is very effective for classification, though deep networks such as ResNet50 and InceptionV3 take significantly longer training time than GoogleNet.