Microgels offer broad applications in bioengineering due to their customizable properties, supporting innovations in mechanobiology, tissue engineering, drug delivery, and cell therapy. This study focuses on characterizing ionically cross-linked alginate microgels using a nanoindentation technique, enabling precise assessment of their mechanical properties at the microscale. We report on the microfluidic fabrication of alginate microgels with varying sizes at different cross-linker concentrations and on the mechanical characterization of the resulting microgels in terms of Young's moduli as well as viscoelastic behavior. Measurements conducted using dynamic nanoindentation reveal that microgel elasticity is strongly influenced by the ionic composition of the surrounding media, in particular, the concentration of calcium and sodium. We demonstrate that the highest Young's modulus observed for ionically cross-linked alginate microgels is in deionized water (7.2 ± 0.9 kPa). A drastic softening effect is observed when the calcium cross-linked microgels are placed into a storage buffer containing divalent ions (0.7 ± 0.1 kPa) and cell culture media consisting of Dulbecco's Modified Eagle Medium (0.2 ± 0.1 kPa) with fetal bovine serum (0.4 ± 0.1 kPa). High concentrations of sodium were found to disrupt ionic cross-links, decreasing stiffness and increasing viscosity, with reversible effects observed upon switching back to deionized water. These findings highlight the importance of media selection for applications requiring mechanical stability, and we provide guidelines for measuring the mechanical properties of microgels in a robust manner that is applicable to a wide range of different conditions.