Privacy-preserving machine learning (PPML) enables clients to collaboratively train deep learning models without sharing private datasets, but faces privacy leakage risks due to gradient leakage attacks. Prevailing methods leverage secure aggregation strategies to enhance PPML, where clients leverage masks and secret sharing to further protect gradient data while tolerating participant dropouts. These methods, however, require frequent inter-client communication to negotiate keys and perform secret sharing, leading to substantial communication overhead. To tackle this issue, we propose NET-SA, an efficient secure aggregation architecture for PPML based on in-network computing. NET-SA employs seed homomorphic pseudorandom generators for local gradient masking and utilizes programmable switches for seed aggregation. Accurate and secure gradient aggregation is then performed on the central server based on masked gradients and aggregated seeds. This design effectively reduces communication overhead due to eliminating the communication-intensive phases of seed agreement and secret sharing, with enhanced dropout tolerance due to overcoming the threshold limit of secret sharing. Extensive experiments on server clusters and Intel Tofino programmable switch demonstrate that NET-SA achieves up to 77x and 12x enhancements in runtime and 2x decrease in total client communication cost compared with state-of-the-art methods.