Current limitations in cardiac tissue engineering revolve around the inability to fully recapitulate the structural organization and mechanical environment of native cardiac tissue. This study aims at developing organized ultrafine fiber scaffolds with improved biocompatibility and architecture in comparison to the traditional fiber scaffolds obtained by solution electrospinning. This is achieved by combining the additive manufacturing of a hydroxyl‐functionalized polyester, (poly(hydroxymethylglycolide‐co‐ε‐caprolactone) (pHMGCL), with melt electrospinning writing (MEW). The use of pHMGCL with MEW vastly improves the cellular response to the mechanical anisotropy. Cardiac progenitor cells (CPCs) are able to align more efficiently along the preferential direction of the melt electrospun pHMGCL fiber scaffolds in comparison to electrospun poly(ε‐caprolactone)‐based scaffolds. Overall, this study describes for the first time that highly ordered microfiber (4.0–7.0 µm) scaffolds based on pHMGCL can be reproducibly generated with MEW and that these scaffolds can support and guide the growth of CPCs and thereby potentially enhance their therapeutic potential.