In engineered heart tissues (EHT), oxygen and nutrient supply via mere diffusion is a likely factor limiting the thickness of cardiac muscle strands. Here, we report on a novel method to in vitro perfuse EHT through tubular channels. Adapting our previously published protocols, we expanded a miniaturized fibrin-based EHT-format to a larger six-well format with six flexible silicone posts holding each EHT (15×25×3 mm³). Thin dry alginate fibers (17×0.04×0.04 mm) were embedded into the cell-fibrin-thrombin mix and, after fibrin polymerization, dissolved by incubation in alginate lyase or sodium citrate. Oxygen concentrations were measured with a microsensor in 14-day-old EHTs (37°C, 21% oxygen) and ranged between 9% at the edges and 2% in the center of the tissue. Perfusion rapidly increased it to 10%-12% in the immediate vicinity of the microchannel. Continuous perfusion (20 μL/h, for 3 weeks) of the tubular lumina (100-500 μm) via hollow posts of the silicone rack increased mean dystrophin-positive cardiomyocyte density (36%±6% vs. 10%±3% of total cell number) and cross sectional area (73±2 vs. 48±1 μm²) in the central part of the tissue compared to nonperfused EHTs. The channels were populated by endothelial cells present in the reconstitution cell mix. In conclusion, we developed a novel approach to generate small tubular structures suitable for perfusion of spontaneously contracting and force-generating EHTs and showed that prolonged perfusion improved cardiac tissue structure.