The objectives of our study were to (a) evaluate the feasibility of using 3D printed phantoms in magnetic resonance imaging (MR) in assessing the robustness and repeatability of radiomic parameters and (b) to compare the results obtained from the 3D printed phantoms to metrics obtained in biological phantoms. To this end, three different 3D phantoms were printed: a Hilbert cube (5 × 5 × 5 cm3) and two cubic quick response (QR) code phantoms (a large phantom (large QR) (5 × 5 × 4 cm3) and a small phantom (small QR) (4 × 4 × 3 cm3)). All 3D printed and biological phantoms (kiwis, tomatoes, and onions) were scanned thrice on clinical 1.5 T and 3 T MR with 1 mm and 2 mm isotropic resolution. Subsequent analyses included analyses of several radiomics indices (RI), their repeatability and reliability were calculated using the coefficient of variation (CV), the relative percentage difference (RPD), and the interclass coefficient (ICC) parameters. Additionally, the readability of QR codes obtained from the MR images was examined with several mobile phones and algorithms. The best repeatability (CV ≤ 10%) is reported for the acquisition protocols with the highest spatial resolution. In general, the repeatability and reliability of RI were better in data obtained at 1.5 T (CV = 1.9) than at 3 T (CV = 2.11). Furthermore, we report good agreements between results obtained for the 3D phantoms and biological phantoms. Finally, analyses of the read-out rate of the QR code revealed better texture analyses for images with a spatial resolution of 1 mm than 2 mm. In conclusion, 3D printing techniques offer a unique solution to create textures for analyzing the reliability of radiomic data from MR scans.