Supramolecular materials based on hydrogen bonding ureido-pyrimidinones (UPy) are highly versatile substrates for tissue engineering, as they provide a platform in which specific functions can be introduced in a modular fashion by means of components with matching supramolecular motifs. In this work, a core-shell fiber mesh is generated by coaxial electrospinning of a robust elastomeric UPy-poly(hexamethylene carbonate) (UPy-PC) core with a hydrophilic shell of poly(ethylene glycol) (UPy-PEG), which is exploited to confer drug release properties to the load-bearing core. The effect of PEG chain length and supramolecular crosslink density on mechanical properties and drug elution profiles is investigated. Hydrated UPy-PC/UPy-PEG meshes containing 30 mol% of UPy-PEG have a Young's modulus matching that of UPy-PC meshes of approximately 0.5 MPa, and elongation at break of 600%. Drug release experiments with low molecular weight drugs encapsulated in the UPy-PEG shell during electrospinning reveal a combined role of drug and matrix hydrophilicity on the elution profile. Our results indicate that a hydrophobic drug is retained in the UPy-PEG shell for several days with a maximum drug release of 56 ± 8% after 14 days, a highly water soluble drug undergoes burst release within one day, and the UPy-modification of a highly water soluble compound increases its retention in the UPy-PEG shell up to multiple weeks. Taken together, our results indicate that the proposed multi-component system is a drug delivery vehicle of excellent versatility for applications requiring strong and durable materials.