Amphiphilic hydrogels are widely reported as systems with great potential for controlled drug release. Nevertheless, the majority of studies make use of functionalization or attachment of drugs to the polymer chains. In this study, we propose a strategy of combining amphiphilic polyurethanes with pH-responsive drugs to develop smart drug carriers. While the amphiphilic character of the polymer imparts an efficient load of hydrophobic and hydrophilic drugs, the drug’s characteristics determine the selectivity of the medium delivery. Drug loading and release behavior as well as hydrolytic degradation of chemically crosslinked polyurethane hydrogels based on PEG and PCL-triol (PU (polyurethane) hydrogels) synthesized by an easy one-pot route were studied. PU hydrogels have been shown to successfully load the hydrophobic acidic drug sodium diclofenac, reaching a partition coefficient of 8 between the most hydrophobic PU and diclofenac/ethanol solutions. Moreover, an oral administration simulation was conducted by changing the environment from an acidic to a neutral medium. PU hydrogels release less than 5% of the drug in an acidic medium; however, in a PBS pH 7.4 solution, diclofenac is delivered in a sustained fashion for up to 40 h, achieving 80% of cumulative release.