The surging demand for machine learning (ML) applications has emphasized the pressing need for efficient ML accelerators capable of addressing the computational and energy demands of increasingly complex ML models. However, the conventional monolithic design of large-scale ML accelerators on a single chip often entails prohibitively high fabrication costs. To address this challenge, this paper proposes a 2.5D chiplet-based architecture based on a silicon photonic interposer, called SwInt, to enable high bandwidth, low latency, and energy-efficient data movement on the interposer, for ML applications. Existing silicon photonic interposer implementations suffer from high power consumption attributed to their inefficient network designs, primarily relying on bus-based communication. Bus-based communication is not scalable, as it suffers from high power consumption of the optical laser due to cumulative losses on the readers and writers when the bandwidth per waveguide (i.e., wavelength division multiplexing degree) increases or the number of processing elements in ML accelerators scales up. SwInt incorporates a novel switch-based network designed using Mach-Zehnder Interferometer (MZI)-based switch cells for offering scalable interposer communication and reducing power consumption. The designed switch architecture avoids blocking using an efficient design, while minimizing the number of stages to offer a low-loss switch. Furthermore, the MZI switch cells are designed with a dividing state, enabling energy-efficient broadcast communication over the interposer and supporting broadcasting demand in ML accelerators. Additionally, we optimized and fabricated silicon photonic devices, Microring Resonators (MRRs) and MZIs, which are integral components of our network architecture. Our analysis shows that SwInt achieves, on average, 62% and 64% improvement in power consumption under, respectively, unicast and broadcast communication, resulting in 59.7% energy-efficiency improvement compared to the state-of-the-art silicon photonic interposers specifically designed for ML accelerators.