Fiber-shaped soft constructs are indispensable building blocks for various 3D functional objects such as hierarchical structures within the human body. The design and fabrication of such hierarchically structured soft materials, however, are often challenged by the trade-offs between stiffness, toughness, and continuous production. Here, we describe a microfluidic platform to continuously fabricate double network hydrogel microfibers with tunable structural, chemical, and mechanical features. Construction of the double network microfibers is accomplished through the incorporation of dynamic cucurbit[n]uril host-guest interactions, as energy dissipation moieties, within an agar-based brittle network. These microfibers exhibit an increase in fracture stress, stretchability, and toughness by 2-3 orders of magnitude compared to the pristine agar network, while simultaneously gaining recoverable hysteretic energy dissipation without sacrificing mechanical strength. This strategy of integrating a wide range of dynamic interactions with the breadth of natural resources could be used in the preparation of functional hydrogels, providing a versatile approach toward the continuous fabrication of soft materials with programmable functions.