Mechanobiological cues influence chondrocyte biosynthesis and are often used in tissue engineering applications to improve the repair of articular cartilage in load‐bearing joints. In this work, the biophysical effects of an applied dynamic compression on chondrocytes encapsulated in viscoelastic hydrazone covalent adaptable networks (CANs) is explored. Here, hydrazone CANs exhibit viscoelastic loss tangents ranging from (9.03 ± 0.01) 10–4 to (1.67 ± 0.09) 10–3 based on the molar percentages of alkyl‐hydrazone and benzyl‐hydrazone crosslinks. Notably, viscoelastic alkyl‐hydrazone crosslinks improve articular cartilage specific gene expression showing higher SOX9 expression in free swelling hydrogels and dynamic compression reduces hypertrophic chondrocyte markers (COL10A1, MMP13) in hydrazone CANs. Interestingly, dynamic compression also improves matrix biosynthesis in elastic benzyl‐hydrazone controls but reduces biosynthesis in viscoelastic alkyl‐hydrazone CANs. Additionally, intermediate levels of viscoelastic adaptability demonstrate the highest levels of matrix biosynthesis in hydrazone CANs, demonstrating on average 70 ± 4 µg of sulfated glycosaminoglycans per day and 31 ± 3 µg of collagen per day over one month in dynamic compression bioreactors. Collectively, the results herein demonstrate the role of matrix adaptability and viscoelasticity on chondrocytes in hydrazone CANs during dynamic compression, which may prove useful for tissue engineering applications in load‐bearing joints.